]>
2018
11
6
ISSN 2008-1898
142
On \(m\)-skew complex symmetric operators
On \(m\)-skew complex symmetric operators
en
en
In this paper, the definition of \(m\)-skew complex symmetric operators is introduced. Firstly, we
prove that \(\Delta_{m}^{-}(T)\) is complex symmetric with the
conjugation \(C\) and give some properties of \(\Delta_{m}^{-}(T)\).
Secondly, let \(T\) be \(m\)-skew complex symmetric
with conjugation \(C\), if \(n\) is odd, then \(T^{n}\) is \(m\)-skew complex symmetric
with conjugation \(C\); if \(n\) is even, with the assumption \(T^{*}CTC=CTCT^{*}\),
then \(T^{n}\) is \(m\)-complex symmetric
with conjugation \(C\). Finally, we give some properties of \(m\)-skew complex
symmetric operators.
734
745
Haiying
Li
School of Mathematics and Information Science
Henan Normal University
P. R. China
haiyingli2012@yahoo.com
Yaru
Wang
School of Mathematics and Information Science
Henan Normal University
P. R. China
2695527694@qq.com
\(m\)-skew complex symmetric operator
conjugation
spectral
Article.1.pdf
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M. Cho, E. Ko, J. E. Lee, On m-complex symmetric operators, Mediter. J. Math., 13 (2016), 2025-2038
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M. Cho, E. Ko, J. E. Lee, On m-complex symmetric operators II, Mediter. J. Math., 13 (2016), 3255-3264
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M. Cho, E. Ko, J. E. Lee, Properties of m-complex symmetric operators, Stud. Univ. Babeş-Bolyai Math., 62 (2017), 233-248
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J. B. Conway, A course in functional analysis, Second edition, Springer-Verlag, New York, (1990), -
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S. R. Garcia, E. Prodan, M. Putinar, Mathematical and physical aspects of complex symmetric operators, J. Phys. A, 2014 (2014), 1-54
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P. V. Hai, L. H. Khoi, Complex symmetry of weighted composition operators on the Fock space, J. Math. Anal. Appl., 433 (2016), 1757-1771
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E. Ko, E. Ko, J. E. Lee, Skew complex symmetric operator and Weyl type theorems, Bull. Korean Math. Soc., 52 (2015), 1269-1283
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E. Ko, J. E. Lee, On complex symmetric Toeplitz operators, J. Math. Anal. Appl., 434 (2016), 20-34
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X. Wang, Z. Gao, A note on Aluthge transforms of complex symmetric operators and applications, Integral Equations Operator Theory, 65 (2009), 573-580
]
The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces
The generalized viscosity implicit rule of nonexpansive semigroup in Banach spaces
en
en
In this research, we focus on a common fixed point problem of a
nonexpansive semigroup with the generalized viscosity methods for
implicit iterative algorithms. Our main objective is to construct
the new strong convergence theorems under certain appropriate
conditions in uniformly convex and uniformly smooth Banach spaces.
Specifically, the main results make a contribution to the implicit
midpoint theorems. The findings for theorems in Hilbert spaces and
the other forms of a nonexpansive semigroup can be used in several
practical purposes. Finally, a numerical example in 3 dimensions is
provided to support our main results.
746
761
Chaichana
Jaiboon
Department of Mathematics, Faculty of Liberal Arts
Rajamangala University of Technology Rattanakosin
Thailand
chaichana.jai@rmutr.ac.th
Somyot
Plubtieng
Department of Mathematics, Faculty of Science
Naresuan University
Thailand
somyotp@nu.ac.th
Phayap
Katchang
Rajamangala University of Technology Lanna Tak
Division of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak 63000, Thailand
Thailand
p.katchang@rmutl.ac.th
Nonexpansive semigroup
fixed point
generalized viscosity
implicit
Banach space
Article.2.pdf
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[1]
S. Atsushiba, W. Takahashi , Strong convergence of Mann’s-type iterations for nonexpansive semigroups in general Banach spaces, Nonlinear Anal., 61 (2005), 881-899
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W.-B. Guan , An iterative method for variational inequality problems, J. Inequal. Appl., 2013 (2013), 1-10
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Y. Ke, C. Ma , The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-21
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A. T.-M. Lau, Amenability and fixed point property for semigroup of nonexpansive mapping, Fixed point theory Appl. (Marseille, (1989)), Pitman Res. Notes Math. Ser. Longman Sci. Tech., Harlow (1991)
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##[8]
P. Sunthrayuth, P. Kumam, Viscosity approximation methods based on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces, Math. Comput. Modelling, 58 (2013), 1814-1828
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T. Suzuki , Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl., 305 (2005), 227-239
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H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-12
##[14]
Q. Yan, G. Cai, P. Luo , Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces, J. Nonlinear Sci. Appl., 9 (2016), 4039-4051
]
On Brunn-Minkowski type inequality
On Brunn-Minkowski type inequality
en
en
The notion of Aleksandrov body in the classical Brunn-Minkowski theory is extended to that
of Orlicz-Aleksandrov body in the Orlicz Brunn-Minkowski theory. The analogs of the Brunn-Minkowski type inequality and the first variations of volume are established via Orlicz-Aleksandrov body. We also make some considerations for the polar of Orlicz combination.
762
769
Lewen
Ji
Department of Mathematics
Department of Mathematics
East China University of Technology
Shanghai University
China
China
jilewen2008@163.com
Zhenbing
Zeng
Department of Mathematics
Shanghai University
China
zbzeng@shu.edu.cn
Jingjing
Zhong
School of Public Finance and Public Administration
Jiangxi University of Finance and Economics
China
33515343@qq.com
Orlicz-Aleksandrov body
Brunn-Minkowski type inequality
Orlicz combination
Article.3.pdf
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A. D. Aleksandrov, On the theory of mixed volumes.I. Extension of certain concepts in the theory of convex bodies, Mat. Sb., 2 (1937), 947-972
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]
Sharp generalized Papenfuss-Bach-type inequality
Sharp generalized Papenfuss-Bach-type inequality
en
en
In this paper, we prove and develop a conjecture on the generalized double
Papenfuss-Bach inequality proposed by Sun and Zhu [Z. Sun, L. Zhu, J. Appl. Math., \(\textbf{2011}\) (2011), 9 pages]. In the last section
we pose a conjecture on a general form of Papenfuss-Bach-type inequality.
770
777
Ling
Zhu
Department of Mathematics
Zhejiang Gongshang University
China
zhuling0571@163.com
Circular approximation
Bernoulli numbers
Papenfuss-Bach inequality
Article.4.pdf
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]
Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process
Asymptotic behavior of parametric estimation for a class of nonlinear diffusion process
en
en
In this paper, a stochastic process, which is a class of nonhomogeneous diffusion process from the perspective of the corresponding nonlinear stochastic differential equation is studied. The parameter included in the drift term
are estimated by sequential maximum likelihood methodology. The sequential estimators are proved to be closed, unbiased, strongly consistent, normally distributed, and optimal in the mean square sense.
778
784
Chenglian
Zhu
School of Mathematical Science
Huaiyin Normal University
P. R. China
hynuzcl@126.com
Nonlinear diffusion process
sequential maximum likelihood estimation
mean square sense
Article.5.pdf
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C. Lee, J. P. N. Bishwal, M. H. Lee, Sequential maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes, J. Statist. Plann. Inference, 142 (2012), 1234-1242
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R. S. Liptser, A. N. Shiryayev, Statistics of random processes I , General Theory, Springer-Verlag, New York (1977)
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]
Dynamics of the zeros of analytic continued polynomials and differential equations associated with \(q\)-tangent polynomials
Dynamics of the zeros of analytic continued polynomials and differential equations associated with \(q\)-tangent polynomials
en
en
In this paper, we study the analytic continuation \(T_q(s)\) and \(T_q(s,w)\) of the \(q\)-Tangent numbers \(T_{n, q}\) and \(q\)-Tangent polynomials \(T_{n, q}(x)\) introduced by authors.
The new concept of dynamics of the zeros of
analytic continued \(q\)-tangent polynomials is investigated observing an
interesting phenomenon of `scattering' of the zeros of \(T_q(s,
w)\). Finally, we study linear differential equations arising from the generating functions of \(q\)-tangent polynomials giving explicit identities for the \(q\)-tangent polynomials.
785
797
Cheon Seoung
Ryoo
Department of Mathematics
Hannam University
Republic of Korea
ryoocs@hnu.kr
Kyung Won
Hwang
Department of Mathematics
Dong-A University
Republic of Korea
khwang@dau.ac.kr
Do Jin
Kim
Department of Mathematics
Kyungpook National University
Republic of Korea
kimdojin@knu.ac.kr
Nam Soon
Jung
College of Talmage Liberal Arts
Hannam University,
Republic of Korea
soonjn@gmail.com
Tangent numbers and polynomials
\(q\)-tangent polynomial
\(q\)-tangent Zeta function
analytic continuation
analytic continued \(q\)-tangent polynomials
zeros
differential equations
Article.6.pdf
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R. Ayoub, Euler and the zeta function, Amer. Math., Monthly, 81 (1974), 1067-1086
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]
Adams-Spanne type estimates for parabolic sublinear operators and their commutators with rough kernels on parabolic generalized Morrey spaces
Adams-Spanne type estimates for parabolic sublinear operators and their commutators with rough kernels on parabolic generalized Morrey spaces
en
en
The aim of this paper is to give Adams-Spanne type estimates for parabolic
sublinear operators and their commutators by with rough kernels generated by
parabolic fractional integral operators under generic size conditions which
are satisfied by most of the operators in harmonic analysis. Their endpoint
estimates are also disposed.
798
811
Ferit
Gürbüz
Department of Mathematics Education, Faculty of Education
Hakkary Uinversity
Turkey
feritgurbuz@hakkari.edu.tr
Parabolic sublinear operator
parabolic fractional integral operator
parabolic fractional maximal operator
rough kernel
parabolic generalized Morrey space
parabolic BMO space
commutator
Article.7.pdf
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D. R. Adams , A note on Riesz potentials, Duke Math. J., 42 (1975), 765-778
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]
Generalized results of majorization inequality via Lidstone's polynomial and newly Green functions
Generalized results of majorization inequality via Lidstone's polynomial and newly Green functions
en
en
Generalized results of majorization inequality are obtained by using newly Green functions defined in [N. Mahmood, R. P. Agarwal, S. I. Butt, J. Pečarić, J. Inequal. Appl., \({\bf2017}\) (2017), 17 pages]
and Lidstone's polynomial. We find
new upper bounds of Grüss and Ostrowski type.
We give further results of majorization inequality by making linear functionals constructed on convex functions \(\frac{f(x)}{x}\).
Some applications are given.
812
831
Nouman
Siddique
Department of Mathematics
Govt. College University
Pakistan
nouman6522@gmail.com
Naveed
Latif
General Studies Department
Jubail Industrial College
Kingdom of Saudi Arabia
naveed707@gmail.com
Josip
Pečarić
Faculty of Textile Technology Zagreb
University of Zagreb
RUDN University
Croatia
Russia
pecaric@element.hr
Classical majorization theorem
Fuchs's thorem
Lidstone's interpolating polynomial
Green Function for 'two point right focal' problem
Čebyšev functional
Grüss type upper bounds
Ostrowski-type bounds
convex function \(f(x)/x\)
n-exponentially convex function
mean value theorems
Stolarsky type means
Article.8.pdf
[
[1]
R. P. Agarwal, S. I. Bradanović, J. Pečarić , Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial, J. Inequal. Appl., 2016 (2016), 1-18
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G. Aras-Gazić, V. Čuljak, J. Pečarić, A. Vukelić , Generalization of Jensen’s inequality by Lidstone’s polynomial and related results, Math. Inequal. Appl., 16 (2013), 1243-1267
##[4]
P. Cerone , On Čebyšev functional bounds , Differential & difference equations and applications, 267-277, Hindawi Publ. Corp., New York (2006)
##[5]
P. Cerone, S. S. Dragomir, Some new Ostrowski-type bounds for the Čebyšev functional and applications, J. Math. Inequal., 8 (2014), 159-170
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]
\(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator
\(BL_{p,\nu}^{m}\) estimates for the Riesz transforms associated with Laplace-Bessel operator
en
en
In this paper, we introduce higher order Riesz-Bessel transforms which
we can express partial derivatives of order \(\alpha\) of \(I_{m,\nu}f\) for \(f\in L_{p,\nu}\).
In addition, we establish relationship between Riesz potential
with higher order Riesz-Bessel transform related to generalized shift operator.
By using this relationship, we make some improvements of integral estimates
for \(I_{m,\nu}f\) and higher order Riesz-Bessel transform \(R_{\nu}^{m}\) in the
Beppo Levi space \(BL_{p,\nu}^{m}\). We prove an estimate for the singular integral operator with
convolution type generated by generalized shift operator in the Beppo Levi spaces.
832
840
Ismail
Ekincioglu
Department of Mathematics Kutahya
Dumlupnar University
Turkey
ismail.ekincioglu@dpu.edu.tr
Cansu
Keskin
Department of Mathematics Kutahya
Dumlupnar University
Turkey
cansu.keskin@dpu.edu.tr
Serap
Guner
Department of Mathematics Kutahya
Dumlupnar University
Turkey
serap.matematik@hotmail.com
Laplace-Bessel operator
Bessel generalized shift operator
Riesz-Bessel transform
fractional integral operator
Beppo Levi spaces
Article.9.pdf
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]
Schur convexity properties for a class of symmetric functions with applications
Schur convexity properties for a class of symmetric functions with applications
en
en
In the article, we prove that the symmetric function
\[
F_{n}\left(x_{1}, x_{2}, \cdots, x_{n}; r\right)=\sum_{1\leq i_{1}<i_{2}<\cdots<i_{r}\leq n}\prod_{j=1}^{r}\left(\frac{1+x_{i_{j}}}{1-x_{i_{j}}}\right)^{1/r}
\]
is Schur convex, Schur multiplicatively convex and Schur harmonic convex on \([0, 1)^{n}\), and establish several new analytic
inequalities by use of the theory of majorization, where \(r\in \{1, 2, \cdots, n\}\) and \(i_{1}, i_{2}, \cdots i_{n}\) are integers.
841
849
Wei-Mao
Qian
School of Distance Education
Huzhou Broadcast and TV University
China
qwm661977@126.com
Yu-Ming
Chu
Department of Mathematics
Huzhou University
China
chuyuming2005@126.com
Schur convex
Schur multiplicatively convex
Schur harmonic convex
symmetric function
Article.10.pdf
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]
Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion
Controllability of time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion
en
en
In this paper, we consider the controllability of certain class of
non-autonomous neutral evolution stochastic functional
differential equations, with time varying delays, driven by a
fractional Brownian motion in a separable real Hilbert space.
Sufficient conditions for controllability are obtained by employing
a fixed point approach. A practical example is provided to
illustrate the viability of the abstract result of this work.
850
863
El Hassan
Lakhel
National School of Applied Sciences
Cadi Ayyad University
Morocco
e.lakhel@uca.ma
Abdelmonaim
Tlidi
National School of Applied Sciences
Cadi Ayyad University
Morocco
mtlidi2010@gmail.com
Controllability
neutral stochastic functional differential equations
evolution operator
fractional Brownian motion
Article.11.pdf
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]
A note on double Laplace decomposition method for solving singular one dimensional pseudo thermo-elasticity coupled system
A note on double Laplace decomposition method for solving singular one dimensional pseudo thermo-elasticity coupled system
en
en
In this paper, Adomain decomposition method is reintroduced with double
Laplace transform methods to obtain closed form solutions of linear and
nonlinear singular one dimensional pseudo thermo-elasticity coupled system.
The nonlinear terms can be easily handled by the use of Adomian polynomials.
Furthermore, we illustrate our proposed methods by one example.
864
876
Hassan
Eltayeb
Mathematics Department, College of Science
King Saud University
Saudi Arabia
hgadain@ksu.edu.sa
Imed
Bachar
Mathematics Department, College of Science
King Saud University
Saudi Arabia
abachar@ksu.edu.sa
Double Laplace transform
inverse Laplace transform
pseudo thermo-elasticity equation
single Laplace transform
decomposition methods
Article.12.pdf
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]