]>
2016
9
9
ISSN 2008-1898
180
Regularized gradient-projection methods for finding the minimum-norm solution of equilibrium and the constrained convex minimization problem
Regularized gradient-projection methods for finding the minimum-norm solution of equilibrium and the constrained convex minimization problem
en
en
The gradient-projection algorithm (GPA) is an effective method for solving the constrained convex
minimization problem. Ordinarily, under some conditions, the minimization problem has more than one
solution, so the regulation is used to find the minimum-norm solution of the minimization problem. In
this article, we come up with a regularized gradient-projection algorithm to find a common element of the
solution set of equilibrium and the solution set of the constrained convex minimization problem, which is
the minimum-norm solution of equilibrium and the constrained convex minimization problem. Under some
suitable conditions, we can obtain some strong convergence theorems. As an application, we apply our
algorithm to solve the split feasibility problem and the constrained convex minimization problem in Hilbert
spaces.
5316
5331
Ming
Tian
College of Since
Tianjin Key Laboratory for Advanced Signal Processing
Civil Aviation University of China
Civil Aviation University of China
China
China
tianming1963@126.com
Hui-Fang
Zhang
College of Since
Civil Aviation University of China
China
huifangzhang109@126.com
Iterative method
equilibrium problem
constrained convex minimization problem
variational inequality
regularization
minimum-norm.
Article.1.pdf
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M. Tian, L. Liu, General iterative methods for equilibrium and constrained convex minimization problem, Optimization, 63 (2014), 1367-1385
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H. K. Xu, Averaged mappings and the gradient-projection algorithm, J. Optim. Theory Appl., 150 (2001), 360-378
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H. K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
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H. K. Xu, Averaged mappings and the gradient-projection algorithm, J. Optim. Theory Appl., 150 (2011), 360-378
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I. Yamada, The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications, Haifa, (2000), Stud. Comput. Math., North-Holland, Amsterdam, 8 (2001), 473-504
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Y. H. Yao, R. P. Agarwal, M. Postolache, Y. C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory and Appl., 2014 (2014), 1-14
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Z. T. Yu, L. J. Lin, C. S. Chuang, A unified study of the split feasible problems with applications, J. Nonlinear Convex Anal., 15 (2014), 605-622
]
Strong convergence results for the split common fixed point problem
Strong convergence results for the split common fixed point problem
en
en
Recently, Boikanyo [O. A. Boikanyo, Appl. Math. Comput., 265 (2015), 844-853] constructed an
algorithm for demicontractive operators and obtained the strong convergence theorem for the split common
fixed point problem. In this paper, we mainly consider the viscosity iteration algorithm of the algorithm
Boikanyo to approximate the split common fixed point problem, and we get the generated sequence strongly
converges to a solution of this problem. The main results in this paper extend and improve some results of
Boikanyo [O. A. Boikanyo, Appl. Math. Comput., 265 (2015), 844-853] and Cui and Wang [H. H. Cui, F.
H. Wang, Fixed Point Theory Appl., 2014 (2014), 8 pages]. The research highlights of this paper are novel
algorithms and strong convergence results.
5332
5343
Huimin
He
School of Mathematics and Statistics
Xidian University
China
huiminhe@126.com
Sanyang
Liu
School of Mathematics and Statistics
Xidian University
China
Rudong
Chen
Department of Mathematics
Tianjin Polytechnic University
China
Xiaoyin
Wang
Department of Mathematics
Tianjin Polytechnic University
China
wxywxq@163.com
Split common fixed point problem
demicontractive mapping
explicit viscosity algorithm
strong convergence.
Article.2.pdf
[
[1]
O. A. Boikanyo, A strongly convergent algorithm for the split common fixed point problem, Appl. Math. Comput., 265 (2015), 844-853
##[2]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems,, 18 (2002), 441-453
##[3]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
##[4]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem, Nonlinear Anal., 75 (2012), 2116-2125
##[5]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353-2365
##[6]
Y. Censor, Y. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
##[7]
Y. Censor, Y. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084
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Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587-600
##[9]
H. H. Cui, F. H. Wang, Iterative methods for the split common fixed point problem in Hilbert spaces, Fixed Point Theory and Appl., 2014 (2014), 1-8
##[10]
Q. W. Fan, W. Wu, J. M. Zurada, Convergence of batch gradient learning with smoothing regularization and adaptive momentum for neural networks, SpringerPlus, 5 (2016), 1-17
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R. Kraikaew, S. Saejung, On split common fixed point problems, J. Math. Anal. Appl., 415 (2014), 513-524
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B. Qu, B. H. Liu, N. Zheng, On the computation of the step-size for the CQ-like algorithms for the split feasibility problem, Appl. Math. Comput., 262 (2015), 218-223
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B. Qu, N. Xiu, A note on the CQ algorithm for the split feasibility problem, Inverse Problems, 21 (2005), 1655-1665
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W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
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F. H. Wang, H.-K. Xu, Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal., 74 (2011), 4105-4111
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Z. W. Wang, Q. Z. Yang, Y. Yang, The relaxed inexact projection methods for the split feasibility problem, Appl. Math. Comput., 217 (2011), 5347-5359
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H.-K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl., 116 (2003), 659-678
##[23]
H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[24]
H.-K. Xu, A variable Krasonselskiĭ-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22 (2006), 2021-2034
##[25]
Q. Z. Yang, The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems, 20 (2004), 1261-1266
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J. L. Zhao, Q. Z. Yang, Several solution methods for the split feasibility problem, Inverse Problems, 21 (2005), 1791-1799
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J. L. Zhao, Y. J. Zhang, Q. Z. Yang, Modified projection methods for the split feasibility problem and the multiple- sets split feasibility problem, Appl. Math. Comput., 219 (2012), 1644-1653
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Z. C. Zhu, R. Chen, Strong convergence on iterative methods of Cesáro means for nonexpansive mapping in Banach space, Abstr. Appl. Anal., 2014 (2014), 1-6
]
Quadratic \(\rho\)-functional inequalities in complex matrix normed spaces
Quadratic \(\rho\)-functional inequalities in complex matrix normed spaces
en
en
In this paper, we solve the following quadratic \(\rho\) -functional inequalities
\[\|f(x + y)+f(x - y) - 2f(x) - 2f(y)\| \leq\|\rho(2f(\frac{x + y}{2}) + 2f(\frac{x - y}{2}) - f(x) - f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|< 1\), and
\[\|2f(\frac{x + y}{2}) + 2f(\frac{x - y}{2}) - f(x) - f(y)\| \leq\|\rho(f(x + y)+f(x - y) - 2f(x) - 2f(y)\|,\]
where \(\rho\) is a fixed complex number with \(|\rho| <\frac{ 1}{2}\) . By using the direct method, we prove the Hyers-Ulam
stability of these inequalities in complex matrix normed spaces, and prove the Hyers-Ulam stability of
quadratic \(\rho\)-functional equations associated with these inequalities in complex matrix normed spaces.
5344
5352
Zhihua
Wang
School of Science
Hubei University of Technology
P. R. China
matwzh2000@126.com
Choonkil
Park
Research Institute for Natural Sciences
Hanyang University
Republic of Korea
baak@hanyang.ac.kr
Hyers-Ulam stability
matrix normed space
quadratic \(\rho\)-functional equation
quadratic \(\rho\)-functional inequality.
Article.3.pdf
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T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
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P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
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D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27 (1941), 222-224
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S.-Y. Jang, J. R. Lee, C. K. Park, D. Y. Shin, Fuzzy stability of Jensen-type quadratic functional equations, Abstr. Appl. Anal., 2009 (2009), 1-17
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]
Hyperstability of a quadratic functional equation on abelian group and inner product spaces
Hyperstability of a quadratic functional equation on abelian group and inner product spaces
en
en
Using the fixed point approach, we prove some results on hyperstability of the following quadratic
functional equation
\[f(x + y + z) + f(x - y) + f(x - z) + f(y - z) = 3[f(x) + f(y) + f(z)],\]
in the class of functions from an abelian group into a Banach space.
5353
5361
Iz-iddine
EL-Fassi
Department of Mathematics, Faculty of Sciences
University of Ibn Tofail
Morocco
lzidd-math@hotmail.fr
Gwang Hui
Kim
Department of Mathematics
Kangnam University
Republic of Korea
ghkim@kangnam.ac.kr
Hyperstability
quadratic functional equation
fixed point theorem.
Article.4.pdf
[
[1]
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan., 2 (1950), 64-66
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J.-H. Bae, On the stability of 3-dimensional quadratic functional equation, Bull. Korean Math. Soc., 37 (2000), 477-486
##[3]
J.-H. Bae, K.-W. Jun, On the generalized Hyers-Ulam-Rassias stability of a quadratic functional equation, Bull. Korean Math. Soc., 38 (2011), 325-336
##[4]
J.-H. Bae, Y.-S. Jung, The Hyers-Ulam stability of the quadratic functional equations on abelian groups, Bull. Korean Math. Soc., 39 (2002), 199-209
##[5]
A. Bahyrycz, M. Piszczek, Hyperstability of the Jensen functional equation, Acta Math. Hungar., 142 (2014), 353-365
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D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J., 16 (1949), 385-397
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J. Brzdęk, Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar., 141 (2013), 58-67
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J. Brzdęk, Remarks on hyperstability of the Cauchy functional equation, Aequationes Math., 86 (2013), 255-267
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J. Brzdęk, A hyperstability result for the Cauchy equation, Bull. Aust. Math. Soc., 89 (2014), 33-40
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J. Brzdęk, J. Chudziak, Z. Páles, A fixed point approach to stability of functional equations, Nonlinear Anal., 74 (2011), 6728-6732
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J. Brzdęk, K. Ciepliński, Hyperstability and superstability, Abstr. Appl. Anal., 2013 (2013), 1-13
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St. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62 (1992), 59-64
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Iz. EL-Fassi, S. Kabbaj, On the hyperstability of a Cauchy-Jensen type functional equation in Banach spaces, Proyecciones, 34 (2015), 359-375
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P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
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E. Gselmann, Hyperstability of a functional equation, Acta Math. Hungar., 124 (2009), 179-188
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D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A, 27 (1941), 222-224
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S.-M. Jung, On the Hyers-Ulam-Rassias stability of a quadratic functional equation, J. Math. Anal. Appl., 232 (1999), 384-393
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G. Maksa, Z. Páles, Hyperstability of a class of linear functional equations, Acta Math. Acad. Paedagog. Nyhzi. (N.S.), 17 (2001), 107-112
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M. Mirzavaziri, M. S. Moslehian, fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. (N.S.), 37 (2006), 361-376
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M. Piszczek, Remark on hyperstability of the general linear equation, Aequationes Math., 88 (2013), 163-168
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Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
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Th. M. Rassias, On a modified Hyers-Ulam sequence, J. Math. Anal. Appl., 158 (1991), 106-113
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S. M. Ulam, Problems in modern mathematics, Science Editions John Wiley & Sons, Inc., New York (1960)
]
Bipolar metric spaces and some fixed point theorems
Bipolar metric spaces and some fixed point theorems
en
en
In this paper we introduce the concept of bipolar metric space as a type of partial distance. We explore
the link between metric spaces and bipolar metric spaces, especially in the context of completeness, and
prove some extensions of known fixed point theorems.
5362
5373
Ali
Mutlu
Department of Mathematics
Celal Bayar University
Turkey
abgamutlu@gmail.com
Utku
Gürdal
Department of Mathematics
Celal Bayar University
Turkey
utkugurdal@gmail.com
Fixed point
completeness
contraction
metric space
bipolar metric space.
Article.5.pdf
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R. P. Agarwal, M. A. Alghamdi, N. Shahzad, Fixed point theory for cyclic generalized contractions in partial metric spaces, Fixed Point Theory and Appl., 2012 (2012), 1-11
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
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M. M. Deza, E. Deza, Encyclopedia of distances, Springer-Verlag, Berlin (2009)
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Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297
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]
Some new inequalities for (k,s)-fractional integrals
Some new inequalities for (k,s)-fractional integrals
en
en
In this paper, the (k; s)-fractional integral operator is used to generate new classes of integral inequalities
using a family of n positive functions, \((n \in \mathbb{N} )\). Two classes of integral inequalities involving the (k; s)-
fractional integral operator are derived here and these results allow us in particular to generalize some
classical inequalities. Certain interesting consequent results of the main theorems are also pointed out.
5374
5381
M.
Aldhaifallah
Electrical Engineering Department, College of Engineering-Wadi Aldawaser
Prince Sattam bin Abdulaziz University
Saudi Arabia
m.aldhaifallah@psau.edu.sa
M.
Tomar
Department of Mathematics, Faculty of Science and Arts
Ordu University
Turkey
muharremtomar@gmail.com
K. S.
Nisar
Department of Mathematics, College of Arts and Science- Wadi Al-Dawaser
Prince Sattam bin Abdulaziz University
Saudi Arabia
ksnisar1@gmail.com
S. D.
Purohit
Department of HEAS (Mathematics)
Rajasthan Technical University
India
sunil_a_purohit@yahoo.com
Integral inequalities
fractional integral inequalities
(k،s)-fractional integrals.
Article.6.pdf
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A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Thermal Sci., 20 (2016), 763-769
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D. Baleanu, D. Kumar, S. D. Purohit, Generalized fractional integrals of product of two H-functions and a general class of polynomials, Int. J. Comput. Math., 93 (2016), 1320-1329
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D. Baleanu, S. D. Purohit, Chebyshev type integral inequalities involving the fractional hypergeometric operators, Abstr. Appl. Anal., 2014 (2014), 1-10
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D. Baleanu, S. D. Purohit, P. Agarwal, On fractional integral inequalities involving hypergeometric operators, Chin. J. Math. (N.Y.), 2014 (2014), 1-5
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J. S. Choi, S. D. Purohit, A Grüss type integral inequality associated with gauss hypergeometric function fractional integral operator,, Commun. Korean Math. Soc., 30 (2015), 81-92
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]
The Perturbed Riemann Problem for the Chromatography System of Langmuir Isotherm with one Inert Component
The Perturbed Riemann Problem for the Chromatography System of Langmuir Isotherm with one Inert Component
en
en
The solutions of the perturbed Riemann problem for the chromatography system of Langmuir isotherm
with one inert component are constructed in completely explicit forms when the initial data are taken as
three piecewise constant states. The wave interaction problem is investigated in detail by using the method of
characteristics. In addition, the generalized Riemann problem with the delta-type initial data is considered
and the delta contact discontinuity is discovered. Moreover, the strength of delta contact discontinuity
decreases linearly at a constant rate and then the delta contact discontinuity degenerates to be the contact
discontinuity when across the critical point.
5382
5397
Pengpeng
Ji
School of Mathematics and Statistics Science
Ludong University
P. R. China
905099960@qq.com
Chun
Shen
School of Mathematics and Statistics Science
Ludong University, Yantai
P. R. China
shenchun3641@sina.com
Chromatography system
Riemann problem
wave interaction
Temple class
hyperbolic conservation law.
Article.7.pdf
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D. Baleanu, Y. Y. Okur, S. Okur, K. Ocakoglu, Parameter identification of the Langmuir model for adsorption and desorption kinetic data,, Nonlinear Complex Dyn., Springer, New York, 2011 (2011), 97-106
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]
Epinormality
Epinormality
en
en
A topological space \((X ; {\tau} )\) is called epinormal if there is a coarser topology \(\acute{\tau}\) on \(X\) such that \((X ;
\acute{\tau} )\) is \(T_4\). We investigate this property and present some examples to illustrate the relationships between
epinormality and other weaker kinds of normality.
5398
5402
Samirah
AlZahrani
Department of Mathematics
Taif University
Saudi Arabia
mam_1420@hotmail.com;samar.alz@tu.edu.sa
Lutfi
Kalantan
Department of Mathematics
King Abdulaziz University
Saudi Arabia
lk274387@hotmail.com;lkalantan@kau.edu.sa
Normal
epinormal
mildly normal
C-normal
L-normal
submetrizable
regularly closed.
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]
Youngs inequality for multivariate functions
Youngs inequality for multivariate functions
en
en
This paper presents a generalization of Young's inequality to the real functions of several variables.
Moreover, the relevant facts about Young's inequality and its extension including improved proofs are
provided in a review. The basic results are initiated by applying the integral method to a strictly increasing
continuous function of one variable.
5403
5409
Zlatko
Pavić
Mechanical Engineering Faculty in Slavonski Brod
University of Osijek
China
Zlatko.Pavic@sfsb.hr
Strictly increasing function
integral sum
Young's inequality
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]
Stationary distribution of stochastic nuclear spin generator systems
Stationary distribution of stochastic nuclear spin generator systems
en
en
This paper discusses the stochastic nuclear spin generator systems under the in
fluence of white noise.
We prove the existence of a unique solution and a stationary distribution for stochastic nuclear spin generator
systems. We analyze long-time behaviour of random attractor of the distributions of the solutions.
Furthermore, we prove that the random attractor contains of only one point for particular parameters or
can converge weakly to a stationary distribution. Numerical experiments illustrate the results.
5410
5427
Zaitang
Huang
Yangtze Center of Mathematics and Department of Mathematics
Sichuan University
P. R. China
zaitanghuang@163.com
Existence of a unique solution
stationary distribution
random attractor
invariant measure
nuclear spin generator.
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M. R. Molaei, Ö. Umut, Generalized synchronization of nuclear spin generator system, Chaos Solitons Fractals, 37 (2008), 227-232
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]
Solving variational inequality and split equality common fixed-point problem without prior knowledge of operator norms
Solving variational inequality and split equality common fixed-point problem without prior knowledge of operator norms
en
en
In this paper, we introduce a viscosity iterative algorithm for finding common solution of variational
inequality for Lipschitzian and strongly monotone operators and the split equality common fixed-point
problem for firmly quasi-nonexpansive operators. We prove the strong convergence of the proposed algorithm
which does not need any prior information about the bounded linear operator norms.
5428
5440
Jing
Zhao
College of Science
Civil Aviation University of China
P. R. China
zhaojing200103@163.com
Haili
Zong
College of Science
Civil Aviation University of China
P. R. China
Guangxuan
Liu
College of Science
Civil Aviation University of China
P. R. China
Hang
Zhang
College of Science
Civil Aviation University of China
P. R. China
Split equality problem
firmly quasi-nonexpansive operators
strong convergence
viscosity iterative algorithm
Hilbert space.
Article.11.pdf
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H. Attouch, J. Bolte, P. Redont, A. Soubeyran, Alternating proximal algorithms for weakly coupled convex minimization problems, Applications to dynamical games and PDE's, J. Convex Anal., 15 (2008), 485-506
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C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453
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G. Cai, S. Q. Bu, An iterative algorithm for a general system of variational inequalities and fixed point problems in q-uniformly smooth Banach spaces, Optim. Lett., 7 (2013), 267-287
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A. Cegielski, A. Gibali, S. Reich, R. Zalas, An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space, Numer. Funct. Anal. Optim., 34 (2013), 1067-1096
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Y. Censor, T. Elfving , A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
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Y. Censor, A. Gibali, S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms, 59 (2012), 301-323
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Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587-600
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R. D. Chen, J. L. Li, Y. J. Ren, Regularization method for the approximate split equality problem in infinite- dimensional Hilbert spaces, Abstr. Appl. Anal., 2013 (2013), 1-5
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Q.-L. Dong, S. N. He, J. Zhao , Solving the split equality problem without prior knowledge of operator norms, Optimization, 64 (2015), 1887-1906
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S. N. He, C. P. Yang , Solving the variational inequality problem defined on intersection of finite level sets, Abstr. Appl. Anal., 2013 (2013), 1-8
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G. López, V. Martín-Márquez, F. H. Wang, H.-K. Xu, Solving the split feasibility problem without prior knowledge of matrix norms, Inverse Problems, 28 (2012), 1-18
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G. Marino, H.-K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 318 (2006), 43-52
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A. Moudafi, Alternating CQ-algorithms for convex feasibility and split fixed-point problems, J. Nonlinear Convex Anal., 15 (2014), 809-818
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A. Moudafi, E. Al-Shemas, Simultaneous iterative methods for split equality problem, Trans. Math. Program. Appl., 1 (2013), 1-11
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S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings, Appl. Math. Comput., 197 (2008), 548-558
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M. Tian, A general iterative algorithm for nonexpansive mappings in Hilbert spaces, Nonlinear Anal., 73 (2010), 689-694
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S. H. Wang, G. Marino, Y.-C. Liou , Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications, J. Global Optim., 54 (2012), 155-171
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H.-K. Xu , A variable Krasnoselskiĭ-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22 (2006), 2021-2034
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H.-K. Xu, Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Problems, 26 (2010), 1-17
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I. Yamada, The hybrid steepest descent for the variational inequality problems over the intersection of fixed points sets of nonexpansive mapping, Inherently Parallel Algorithms in Feasibility and Optimization and Their Application, Edited by: D. Butnariu, Y. Censor, S. Reich, Elsevier, New York, 2001 (2001), 473-504
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M. Zaknoon , Algorithmic developments for the convex feasibility problem, Ph.D. Thesis, University of Haifa, Haifa, Israel (2003)
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J. Zhao, S. N. He, Viscosity approximation methods for split common fixed-point problem of directed operators, Numer. Funct. Anal. Optim., 36 (2015), 528-547
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J. L. Zhao, Q. Z. Yang, A simple projection method for solving the multiple-sets split feasibility problem, Inverse Probl. Sci. Eng., 21 (2013), 537-546
]
On the intuitionistic fuzzy metric spaces and the intuitionistic fuzzy normed spaces
On the intuitionistic fuzzy metric spaces and the intuitionistic fuzzy normed spaces
en
en
The purpose of this article is to evaluate the definition of a class of intuitionistic fuzzy metric space
which was presented by Park [J. H. Park, Chaos Solitons Fractals, 22 (2004), 1039-1046]. This review is
also appropriate to the definition of a class of intuitionistic fuzzy normed space which was presented by
Saadati and Park [R. Saadati, J. H. Park, Chaos Solitons Fractals, 27 (2006), 331-344].
5441
5448
Xia
Li
Department of Mathematics and Sciences
Hebei GEO University
China
libinghua66@sina.com
Meifang
Guo
Department of Mathematics and Sciences
Hebei GEO University
China
58357160@qq.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
tjsuyongfu@163.com
Fuzzy metric space
fuzzy normed space
intuitionistic fuzzy metric space
intuitionistic fuzzy normed space.
Article.12.pdf
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[1]
M. Abbas, B. Ali, W. Sintunavarat, P. Kumam, Tripled fixed point and tripled coincidence point theorems in intuitionistic fuzzy normed spaces, Fixed Point Theory Appl., 2012 (2012), 1-16
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C. Alaca, D. Turkoghlu, C. Yildiz, , Chaos Solitons Fractals, Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 29 (2006), 1073-1078
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K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96
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S. Chauhan, S. Bhatnagar, S. Radenović, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces, Matematiche (Catania), 68 (2013), 87-98
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S. Chauhan, S. Radenović, M. Imdad, C. Vetro, Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dynamic programming, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 108 (2014), 795-810
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Y. J. Cho, J. Martínez-Moreno, A. Roldán, C. Roldán, Coupled coincidence point theorems in (intuitionistic) fuzzy normed spaces, J. Inequal. Appl., 2013 (2013), 1-11
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D. Çoker , An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), 81-89
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C. Di Bari, C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13 (2005), 973-982
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H. Efe, E. Yiğitb, On strong intuitionistic fuzzy metrics, J. Nonlinear Sci. Appl., 9 (2016), 4016-4038
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C. Ionescu, S. Rezapour, M. E. Samei, Fixed points of some new contractions on intuitionistic fuzzy metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-8
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Semicontinuity of solution mappings for a class of parametric generalized vector equilibrium problems
Semicontinuity of solution mappings for a class of parametric generalized vector equilibrium problems
en
en
In this paper, we discuss the upper and lower semicontinuity of the strong efficient solution mapping,
the weakly efficient solution mapping and the efficient solution mapping to a class of parametric generalized
vector equilibrium problems by using scalarization methods and a new density result.
5449
5462
Jue
Lu
Department of Mathematics
School of Mathematics, Physics and Information Science
Sichuan University
Shaoxing University
China
China
admiral_lu@hotmail.com
Yu
Han
Department of Mathematics
Sichuan University
China
hanyumath@163.com
Nan-Jing
Huang
Department of Mathematics
Sichuan University
China
nanjinghuang@hotmail.com
Parametric generalized vector equilibrium problem
solution mapping
lower semicontinuity
upper semicontinuity.
Article.13.pdf
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]
On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method
On the approximate solution of nonlinear time-fractional KdV equation via modified homotopy analysis Laplace transform method
en
en
The approximate solution of the time-fractional KdV equation (KdV) by using modified homotopy
analysis Laplace transform method, which is a combined form of the Laplace transform and homotopy
analysis methods, is investigated for the first time in this article. Comparison of series solutions between
under a rapid convergence and the optimal values of convergence parameter \(\hbar\) is made. The results through
the \(L_2\) and \(L_\infty\) error norms are also analyzed. The validity,
exibility, and accuracy of the proposed method
is conformed through the numerical computations as well as graphical presentations of the results.
5463
5470
Chong
Li
School of Mines, Key Laboratory of Deep Coal Resource Mining of Ministry of Education
China University of Mining and Technology
China
Amit
Kumar
Department of Mathematics
National Institute of Technology
India
Sunil
Kumar
Department of Mathematics
National Institute of Technology
India
Xiao-Jun
Yang
School of Mechanics and Civil Engineering
China University of Mining and Technology
China
dyangxiaojun@163.com
Time-fractional KdV
homotopy analysis Laplace transform method
homotopy polynomial
approximate solution
optimal value.
Article.14.pdf
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A. Atangana, Extension of the Sumudu homotopy perturbation method to an attractor for one-dimensional Keller- Segel equations, Appl. Math. Model., 39 (2015), 2909-2916
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S. Kumar, A. Kumar, D. Baleanu, Two analytical methods for time-fractional nonlinear coupled Boussinesq- Burger's equations arise in propagation of shallow water waves, Nonlinear Dynam., 85 (2016), 699-715
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]
Singularities of dual hypersurfaces of spacelike hypersurfaces in lightcone and Legendrian duality
Singularities of dual hypersurfaces of spacelike hypersurfaces in lightcone and Legendrian duality
en
en
The theory of the Legendrian singularity is applied for lightcones that are canonically embedded in the
higher-dimensional lightcone and de Sitter space in the Minkowski space-time. The singularities of two
classes of hypersurfaces that are dual to space-like hypersurface in the lightcone under Legendrian dualities
are analyzed in detail.
5471
5487
Meiling
He
School of Mathematical Sciences
Harbin Normal University
P. R. China
hemeilingd@163.com
Yang
Jiang
College of Maths and Systematic Science
Shenyang Normal University
P. R. China
xjiangyang@126.com
Zhigang
Wang
School of Mathematical Sciences
Harbin Normal University
P. R. China
wangzg2003205@163.com
Singularity
Legendrian duality
light-cone frame.
Article.15.pdf
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V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, Vol. I, The classification of critical points, caustics and wave fronts, Translated from the Russian by Ian Porteous and Mark Reynolds, Monographs in Mathematics, Birkhäuser Boston, Inc., Boston (1985)
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On fuzzy normed algebras
On fuzzy normed algebras
en
en
In this paper, a characterization for continuous product in a fuzzy normed algebra is established and
it is proved that any fuzzy normed algebra is with continuous product. Another type of continuity for
the product in a fuzzy normed algebras is introduced and studied. These concepts are illustrated by some
examples. Also, the Cartesian product of fuzzy normed algebras is analyzed.
5488
5496
Tudor
Bînzar
Department of Mathematics
Politehnica University of Timisoara
Romania
tudor.binzar@upt.ro
Flavius
Pater
Department of Mathematics
Politehnica University of Timisoara
Romania
flavius.pater@upt.ro
Sorin
Nădăban
Department of Mathematics and Computer Science
Aurel Vlaicu University of Arad
Romania
snadaban@gmail.com
Fuzzy normed algebra
continuous product
fuzzy normed linear space.
Article.16.pdf
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C. Alegre, S. Romaguera, Characterizations of fuzzy metrizable topological vector spaces and their asymmetric generalization in terms of fuzzy (quasi-)norms, Fuzzy Sets and Systems, 161 (2010), 2182-2192
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R. Ameri, Fuzzy inner product and fuzzy norm of hyperspaces, Iran. J. Fuzzy Syst., 11 (2014), 125-135
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T. Bag, S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11 (2003), 687-705
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T. Bag, S. K. Samanta,, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), 513-547
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T. Bag, S. K. Samanta, A comparative study of fuzzy norms on a linear space, Fuzzy Sets and Systems, 159 (2008), 670-684
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I. Goleţ, On generalized fuzzy normed spaces and coincidence point theorems, Fuzzy Sets and Systems, 161 (2010), 1138-1144
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A. K. Mirmostafaee, Perturbation of generalized derivations in fuzzy Menger normed algebras, Fuzzy Sets and Systems, 195 (2012), 109-117
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S. Nădăban, I. Dzitac, Atomic decompositions of fuzzy normed linear spaces for wavelet applications, Informatica (Vilnius), 25 (2014), 643-662
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B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 314-334
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L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353
]