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2018
18
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Accelerate the Training Process of BP neural Network with CUDA Technology
Accelerate the Training Process of BP neural Network with CUDA Technology
en
en
NVIDIA GPUs is a typical Stream Processor device, and have a high
performance of floating-point operations. CUDA uses a bran-new
computing architecture, and provides greater computing ability for
large scale data computing application than CPU. The learning
algorithm of BP neural network has a high compute-intensive and
rules, and be very suitable for the Stream Processor architecture.
Using CUDA technology, the CUBLAS mathematical library and
self-Kernels library, supported by NV Geforce GTX280 as hardware,
modify the study algorithm ecome parallel, definite a parallel data
structure, and describe the mapping mechanism for computing tasks on
CUDA and the key algorithm. Compare the parallel study algorithm
achieved on GTX280 with the serial algorithm on CPU in a simulation
experiment. Improve
the training time by as much as nearly 15 times.
1
10
Yinfen
Xie
Stream processor
GTX280
CUDA
CUBLAS
BP neural network
Article.1.pdf
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[1]
X. Chu, K. Zhao, M. Wang , Massively parallel network coding on GPUs, In Proceedings of IEEE Int’l Symp. On Performance Computing and Communications Conference, Austin, Texas, (2008), 144-151
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NVIDIA Corporation, NVIDIA CUDA Compute Unified Device Architecture Programming Guide 2.0[EB/OL], http://developer.download.nvidia.com/compute/cuda/2 0/docs/NVIDIA CUDA Programming Guide 2.0.pdf. , (2008)
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J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, J. C. Phillips, GPU computing, Proceedings of the IEEE, 96 (2008), 879-899
##[6]
M. Wen, Research on key technology of stream architecture, National University of Defense Technology, Changsha, 9 (2006), 1-15
##[7]
X. Yang, X. Yan, T. Tang , Research and development of Stream Processor technology, Comput. Eng. Sci., 30 (2008), 114-117
##[8]
J. Yi, Y. Hou, Intelligent control technique, Beijing Industry Press, Beijing (2004)
##[9]
C. Yu, Y. Tang, To improve the training time of BP neural networks, In Proceedings of IEEE Int’l Symp. on Info-tech and Info-net. Beijing, China, 3 (2001), 473-479
##[10]
Y. Zhang, X.-J. Yang, G.-B. Wang, I. Rogers, G. Li, Y. Deng, X.-B. Yan , Scientific computing applications on a stream processor, IEEE International Symposium on Performance Analysis of Systems and software (ISPASS), Austin, TX, USA, (2008), 105-114
]
A note on the \(p\)-adic gamma function and \(q\)-Changhee polynomials
A note on the \(p\)-adic gamma function and \(q\)-Changhee polynomials
en
en
In the present work, we consider the fermionic \(p\)-adic \(q\)-integral of \(p\)%
-adic gamma function and the derivative of \(p\)-adic gamma function
by using their Mahler expansions. The relationship between the \(p\)-adic gamma function and \(%
q \)-Changhee numbers is obtained. A new representation is given for
the \(p\)-adic Euler constant. Also, we study on the relationship
between
\(q\)-Changhee polynomials and \(p\)-adic Euler constant using the fermionic \(p\)-adic \(q\)-integral techniques the idea that the \(q\)-Changhee polynomial.
11
17
Özge Çolakoğlu
Havare
Hamza
Menken
\(p\)-Adic number
\(p\)-adic gamma function
the fermionic \(p\)-adic \(q\)-integral
Mahler coefficients
\(p\)-adic Euler constant
\(q\)-Changhee Polynomials
Article.2.pdf
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[1]
S. Araci, D. Erdal, J. J. Seo, A study on the fermionic p-adic q-integral representation on \(\mathbb{Z}_p\) associated with weighted q-Bernstein and q-Genocchi polynomials, Abstr. Appl. Anal., 2011 (2011), 1-10
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T. Kim, q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys., 14 (2007), 15-27
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T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on \(\mathbb{Z}_p\) , Russ. J. Math. Phys., 16 (2009), 484-491
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T. Kim, Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on \(\mathbb{Z}_p\) , Russ. J. Math. Phys., 16 (2009), 93-96
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D. S. Kim, T. Kim, Daehee numbers and polynomials, Appl. Math. Sci. (Ruse), 7 (2013), 5969-5976
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T. Kim, D. S. Kim, T. Mansour, S.-H. Rim, M. Schork , Umbral calculus and Sheffer sequences of polynomials, J. Math. Phys., 54 (2013), 1-15
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T. Kim, H.-I. Kwon, J. J. Seo , Degenerate q-Changhee polynomials, J. Nonlinear Sci. Appl., 9 (2016), 2389-2393
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T. Kim, T. Mansour, S.-H. Rim, J. J. Seo, A note on q-Changhee Polynomials and Numbers, Adv. Studies Theor. Phys., 8 (2014), 35-41
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V. S. Vladimirov, I. V. Volovich, Superanalysis, I, Differential calculus, (Russian) Teoret. Mat. Fiz., 59 (1984), 3-27
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]
A fixed point theorem on multiplicative metric space with integral-type inequality
A fixed point theorem on multiplicative metric space with integral-type inequality
en
en
In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (\(\mathcal{X},\blacktriangle\)) by the help of integral-type contractions of self-quadruple mappings (SQMs), i.e., for \(\wp_1,\wp_2,\wp_3,\wp_4:\mathcal{X}\rightarrow \mathbb{R}\). For this, we assume that the SQMs are weakly compatible mappings and the pairs \(\big(\wp_1,\wp_3\big)\) and \(\big(\wp_2,\wp_4\big)\) satisfy the property \((CLR_{\wp_3\wp_4})\). Further, two corollaries are produced from our main theorem as special cases. The novelty of these results is that for the unique common fixed point (CFP) of the SQMs \(\wp_1,\wp_2,\wp_3,\wp_4\), we do not need to the assumption of completeness of the MMS \((\mathcal{X},\blacktriangle)\). These results generalize the work of Abdou, [A. A. N. Abdou, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 2244--2257], and many others in the available literature.
18
28
Aziz
Khan
Hasib
Khan
Dumitru
Baleanu
Hossein
Jafari
Tahir Saeed
Khan
Maysaa
Alqurashi
Multiplicative metric space
fractional integral inequalities
fixed point theorems
Article.3.pdf
[
[1]
A. A. N. Abdou, Common fixed point results for compatible-type mappings in multiplicative metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 2244-2257
##[2]
R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116
##[3]
R. P. Agarwal, E. Karapınar, B. Samet, An essential remark on fixed point results on multiplicative metric spaces, Fixed Point Theory Appl., 2016 (2016), 1-3
##[4]
R. P. Agarwal, M. Meehan, D. O’Regan , Fixed point theory and applications, Cambridge University Press, Cambridge (2001)
##[5]
M. U. Ali, T. Kamram, E. Karapınar , An approach to existence of fixed points of generalized contractive multivalued mappings of integral type via admissible mapping, Abstr. Appl. Anal., 2014 (2014), 1-7
##[6]
H. Aydi, E. Karapınar, I. Ş. Yüce, Quadruple fixed point theorems in partially ordered metric spaces depending on another function, Appl. Math., 2012 (2012), 1-16
##[7]
D. Baleanu, R. P. Agarwal, H. Khan, R. A. Khan, H. Jafari, On the existence of solution for fractional differential equations of order \(3 < \delta_1\leq 4\), Adv. Difference Equ., 2015 (2015), 1-9
##[8]
D. Baleanu, H. Khan, H. Jafari, R. A. Khan, M. Alipour, On existence results for solutions of a coupled system of hybrid boundary value problems with hybrid conditions, Adv. Difference Equ., 2015 (2015), 1-14
##[9]
S. Banach, Sur les operation dans les ensembles abstraits et leur application aux equations integrals, Fund. Math., 3 (1922), 133-181
##[10]
V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897
##[11]
M.-F. Bota, A. Petruşel, G. Petruşel, B. Samet, Coupled fixed point theorems for single-valued operators in b-metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-15
##[12]
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536
##[13]
S. Chauhan, H. Aydi, W. Shatanawi, C. Vetro, Some integral type fixed point theorems and an application to systems of functional equations, Vietnam J. Math., 42 (2014), 17-37
##[14]
O. Egea, I. Karacab, Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl., 8 (2015), 237-245
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T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorem on partially ordered metric spaces with applications, Nonlinear Anal., 65 (2006), 1379-1393
##[16]
N. Hussain, H. Isik, M. Abbas , Common fixed point results of generalized almost rational contraction mappings with an application, J. Nonlinear Sci. Appl., 9 (2016), 2273-2288
##[17]
H. Jafari, D. Baleanu, H. Khan, R. A. Khan, A. Khan, Existence criterion for the solutions of fractional order p-Laplacian boundary value problems, Bound. Value Probl., 2015 (2015), 1-10
##[18]
M. Jleli, B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., 2015 (2015), 1-14
##[19]
E. Karapinar, Quartet fixed point for nonlinear contraction, Gen. Topol., 2012 (2012), 1-10
##[20]
H. Khan, H. Jafari, D. Baleanu, R. A. Khan, A. Khan, On iterative solutions and error estimations of a coupled system of fractional order differential-integral equations with initial and boundary conditions, Differ. Equ. Dyn. Syst., 2017 (2017), 1-13
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A. Khan, H. Khan, E. Karapınar, T. S. Khan, Fixed points of weakly compatible mappings satisfying a generalized common limit range property, J. Nonlinear Sci. Appl., 10 (2017), 5690-5700
##[22]
H. Khan, Y. Li, W. Chen, D. Baleanu, A. Khan, Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations withp-Laplacian operator, Bound. Value Probl., 2017 (2017), 1-16
##[23]
H. Khan, Y. Li, H. Sun, A. Khan, Existence of solution and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator, J. Nonlinear Sci. Appl., 10 (2017), 5219-5229
##[24]
X.-L. Liu, Quadruple fixed point theorems in partially ordered metric spaces with mixed g-monotone property, Fixed Point Theory Appl., 2013 (2013), 1-18
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Z. Mustafa, E. Karapınar, H. Aydi, A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces, J. Inequal. Appl., 2014 (2014), 1-12
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S. B. Nadler, Multi-valued contraction mappings, Pac. J. Math., 30 (1969), 475-488
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H. K. Nashine, Common fixed point theorems satisfying integral type rational contractive conditions and applications, Miskolc Math. Notes, 16 (2015), 321-352
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M. Sarwar, M. Bahadur Zada, I. M. Erhan, Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations, Fixed Point Theory Appl., 2015 (2015 ), 1-15
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W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling,, 55 (2012), 680-687
##[30]
M. Stojaković, L. Gajić, T. Došenović, B. Carić, Fixed point of multivalued integral type of contraction mappings, Fixed Point Theory Appl., 2015 (2015), 1-10
]
New Hermite-Hadamard type inequalities for product of different convex functions involving certain fractional integral operators
New Hermite-Hadamard type inequalities for product of different convex functions involving certain fractional integral operators
en
en
We aim to establish new Hermite-Hadamard type inequalities for products of two different convex functions
involving certain generalized fractional integral operators.
The results presented here, being very general, are pointed out to be specialized to yield
many new and known inequalities associated with some known fractional integral operators.
29
36
Erhan
Set
Junesang
Choi
Barıs
Celik
Convex function
\(s\)-convex function
Hermite-Hadamard type inequalities
fractional integral operators
Article.4.pdf
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R. P. Agarwal, M.-J. Luo, R. K. Raina, On Ostrowski type inequalities, Fasc. Math., 56 (2016), 5-27
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M. U. Awan, M. A. Noor, M. V. Mihai, K. I. Noor, Fractional Hermite-Hadamard inequalities for differentiables- Godunova-Levin functions, Filomat, 30 (2016), 3235-3241
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Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonlinear. Sci. Lett. A, 2 (2010), 155-160
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E. Set, A. O. Akdemir, B. Çelik, Some Hermite-Hadamard type inequalities for products of two different convex functions via conformable fractional integrals, Xth International Statistics Days Conference, Turkey (2016)
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E. Set, M. Z. Sarıkaya, M. E. Özdemir, H. Yıldırım, The Hermite-Hadamard’s inequality for some convex functions via fractional integrals and related results, J. Appl. Math. Stat. Inform., 10 (2014), 69-83
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H. M. Srivastava, J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, Amsterdam (2012)
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F. Usta, H. Budak, M. Z. Sarıkaya, E. Set, On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, , (https://www.researchgate.net/publication/312596720), -
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H. Yaldız, M. Z. Sarıkaya, On the Hermite-Hadamard type inequalities for fractional integral operator, , ( https://www. researchgate.net/publication/309824275), -
]
Stability of switched stochastic nonlinear systems by an improved average dwell time method
Stability of switched stochastic nonlinear systems by an improved average dwell time method
en
en
This paper investigates the stability of switched stochastic
continuous-time nonlinear systems in two cases:
(1) all subsystems are global
asymptotically exponentially
stable in the mean (GASiM);
(2) both GASiM subsystems and unstable
subsystems coexist, and proposes a number of new results on the
stability analysis.
Firstly, an improved average dwell time (ADT)
method is established for the stability of switched stochastic
system by extending our previous dwell time method. Especially, an
improved mode-dependent average dwell time (MDADT) method for the
switched stochastic systems whose subsystems are quadratically
stable in the mean is also obtained. Secondly, based on the improved
ADT and MDADT methods, several new results on the stability analysis
are provided. It should be pointed out that the obtained results
have two advantages over the existing results, one is the
conditions of the improved ADT method are simplified, the other is
that the obtained lower bound of ADT \((\tau_a^*)\) is also smaller
than those obtained by other methods. Finally, two illustrative
examples with simulation are given to show the correctness and the
effectiveness of the proposed results.
37
48
Rongwei
Guo
Yuangong
Sun
Ping
Zhao
Switched stochastic nonlinear system
stability in the mean
unstable subsystems
average dwell time
mode-dependent dwell time
Article.5.pdf
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##[5]
R.-W. Guo, Y.-Z. Wang, Input-to-state stability for a class of nonlinear switched systems by minimum dwell time method, Proceedings of the 31st Chinese Control Conference, Hefei, China, (2012), 1383-1386
##[6]
R.-W. Guo, Y.-Z. Wang, Stability analysis for a class of switched linear systems, Asian J. Control, 14 (2012), 817-826
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T. Hou, W.-H. Zhang, H.-J. Ma, Infinite horizon \(H_2/H_\infty\) optimal control for discrete-time Markov jump systems with (x, u, v)-dependent noise, J. Global Optim., 57 (2013), 1245-1262
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H. Lin, P. J. Antsaklis, Stability and stabilizability of switched linear systems: a survey of recent results, IEEE Trans. Automat. Control, 54 (2009), 308-322
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M. A. Müller, D. Liberzon, Input/output-to-state stability and state-norm estimators for switched nonlinear systems, Automatica J. IFAC, 48 (2012), 2029-2039
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J. Qi, Y.-G. Sun, Global exponential stability of certain switched systems with time-varying delays, Appl. Math. Lett., 26 (2013), 760-765
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##[20]
Y.-G. Sun, Stability analysis of positive switched systems via joint linear copositive Lyapunov functions, Nonlinear Anal. Hybrid Syst., 19 (2016), 146-152
##[21]
Y.-G. Sun, L. Wang, On stability of a class of switched nonlinear systems, Automatica J. IFAC, 49 (2013), 305-307
##[22]
Z.-R. Wu, Y.-G. Sun, On easily verifiable conditions for the existence of common linear copositive Lyapunov functions, IEEE Trans. Automat. Control, 58 (2013), 1862-1865
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##[24]
G.-S. Zhai, B. Hu, K. Yasuda, A. N. Michel, Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach, Internat. J. Systems Sci., 32 (2001), 1055-1061
##[25]
L.-X. Zhang, \(H_\infty\) estimation for discrete-time piecewise homogeneous Markov jump linear systems, Automatica J. IFAC, 45 (2009), 2570-2576
##[26]
L.-X. Zhang, H.-J. Gao, Asynchronously switched control of switched linear systems with average dwell time, Automatica J. IFAC, 46 (2010), 953-958
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L.-X. Zhang, P. Shi, E. Boukas, C.-H. Wang, \(H_\infty\) model reduction for uncertain switched linear discrete-time systems, Automatica J. IFAC, 44 (2008), 2944-2949
##[28]
X.-D. Zhao, P. Shi, X.-L. Zheng, L.-X. Zhang, Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone, Automatica J. IFAC, 60 (2015), 193-200
##[29]
X.-D. Zhao, L.-X. Zhang, P. Shi, M. Liu, Stability and stabilization of switched linear systems with mode-dependent average dwell time, IEEE Trans. Automat. Control , 57 (2012), 1809-1815
##[30]
X.-D. Zhao, L.-X. Zhang, P. Shi, M. Liu, Stability of switched positive linear systems with average dwell time switching, Automatica J. IFAC, 48 (2012), 1132-1137
]
Fixed point theorems for generalized \(\alpha\)-\(\psi\) type contractive mappings in b-metric spaces and applications
Fixed point theorems for generalized \(\alpha\)-\(\psi\) type contractive mappings in b-metric spaces and applications
en
en
In this paper, we establish fixed point theorems for a new
generalized \(\alpha\)-\(\psi\) type contractive mapping in complete
b-metric spaces. As applications of our results, we obtain fixed
point theorems on metric space endowed with a partial order or a
graph. We also obtain fixed point theorems for cyclic contractive
mappings. Moreover, an application to integral equation is given
here to illustrate the usability of the obtained results.
49
62
Xianbing
Wu
Leina
Zhao
\(\alpha\)-\(\psi\) contractive mapping
b-metric space
fixed point theorem
Article.6.pdf
[
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109-116
##[2]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014), 941-960
##[3]
H. Alikhani, V. Rakočević, S. Rezapour, N. Shahzad, Fixed points of proximinal valued \(\beta-\psi\)-contractive multifunctions, J. Nonlinear Convex Anal., 16 (2015), 2491-2497
##[4]
H. H. Alsulami, S. Chandok, M. A. Taoudi, I. M. Erhan, Some fixed point theorems for (\(\alpha,\psi\))-rational type contractive mappings, Fixed Point Theory Appl., 2015 (2015 ), 1-12
##[5]
P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized \(\alpha-\psi\)-contractions, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 108 (2014), 519-526
##[6]
J. H. Asl, S. Rezapour, N. Shahzad, On fixed points of \(\alpha-\psi\)-contractive multifunctions, Fixed Point Theory Appl., 2012 (2012), 1-6
##[7]
M. Berzig, E. Karapınar, Note on ''Modified \(\alpha-\psi\)-contractive mappings with applications'', Thai J. Math., 13 (2015), 147-152
##[8]
M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Stud. Univ. Babe- Bolyai Math., 54 (2009), 3-14
##[9]
M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4 (2009), 285-301
##[10]
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Notes on fuzzy fractional Sumudu transform
Notes on fuzzy fractional Sumudu transform
en
en
In this paper, the analytical solutions of fuzzy fractional differential equations (FFDEs) are obtained by using the combination of fractional Sumudu transform (FST) and fuzzy calculus. In this regard, we extend the notation of FST to fuzzy fractional Sumudu transformation (FFST) and discuss its fundamental properties for the fuzzy-valued functions. Besides, a comprehensive study of FFST is also carried out for the different cases of Riemann-Liouville Hukuhara differentiability (H-differentiability) of fuzzy-valued functions. Moreover, to illustrate the capability and pertinence of this transform, solutions of some FFDEs are obtained, revealing its simplicity and efficiency.
63
73
Najeeb Alam
Khan
Oyoon Abdul
Razzaq
Muhammad
Ayaz
Fuzzy function
fractional differential equations
Sumudu transform
H-differentiability
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Some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals
Some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals
en
en
In this paper, we establish some new Hermite-Hadamard type inequalities for \(h\)-convex functions via quantum integral on finite intervals. The results presented here would provide extensions and corrections of those given in earlier works.
74
86
Limin
Yang
Ruiyun
Yang
Hermite-Hadamard type inequalities
\(h\)-convex functions
integral inequalities
quantum calculus
Article.8.pdf
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Y.-M. Bai, F. Qi, Some integral inequalities of the Hermite-Hadamard type for log-convex functions on co-ordinates, J. Nonlinear Sci. Appl., 9 (2016), 5900-5908
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]
A Grüss type inequality for two weighted functions
A Grüss type inequality for two weighted functions
en
en
Since Grüss in 1935 presented the so-called Grüss type inequality,
a variety of its variants and generalizations have been investigated.
Among those things, Dragomir in 2000 established
a Grüss type inequality for a functional with a weighted function.
In this sequel, we aim to present a Grüss type inequality for a functional with two weighted functions.
We also apply our main result to give some other inequalities.
87
93
Junesang
Choi
Grüss type inequality and its generalization
Chebyshev inequality
Grüss type inequality with a weighted function
Grüss type inequality with two weighted functions
synchronous functions
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A note on Furuta type operator equation
A note on Furuta type operator equation
en
en
In this paper, we will show the existence of positive semidefinite solution of
Furuta type operator equation
\[\displaystyle\sum_{j=0}^{n-1}A^{j}XA^{n-j-1}=Y,\] where \(Y\)
can be expressed by a comprehensive form.
94
97
Xiaolin
Zeng
Jian
Shi
Furuta type operator equation
generalized Furuta inequality
positive definite operator and positive semidefinite operator
Article.10.pdf
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[1]
T. Furuta, An extension of order preserving operator inequality, Math. Inequal. Appl., 13 (2010), 49-56
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T. Furuta, Positive semidefinite solutions of the operator equation \(\sum^n_{ j=1} A_{n-j}XA_{j-1} = B\), Linear Algebra Appl., 432 (2010), 949-955
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J. Shi, An application of grand Furuta inequality to a type of operator equation, Global Journal of Mathematical Analysis, 2 (2014), 281-285
]
Coincidence best proximity points for geraghty type proximal cyclic contractions
Coincidence best proximity points for geraghty type proximal cyclic contractions
en
en
In this paper, we study the notions of generalized Geraghty
proximal cyclic contractions for non-self mapping and obtain coincidence best proximity point theorems in the framework of complete metric
spaces. Some examples are given to show the validity of our results. Our results extended and unify many existing results in the literature.
98
114
Somayya
Komal
Azhar
Hussain
Nazra
Sultana
Poom
Kumam
\(\alpha\)-Geraghty proximal contraction of first and second kind
\(\alpha\)-proximal cyclic contraction
\(\alpha\)-proximal admissible maps
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]
Third-order differential sandwich-type results involving the Liu-Owa integral operator
Third-order differential sandwich-type results involving the Liu-Owa integral operator
en
en
Some third-order differential subordination and superordination results are derived for multivalent analytic functions in the open unit disk, which are defined by using the Liu-Owa integral operator. In addition, we obtain new third-order differential sandwich-type results for this operator.
115
131
Huo
Tang
M. K.
Aouf
Shigeyoshi
Owa
Shu-Hai
Li
Differential subordination and superordination
multivalent analytic functions
admissible functions
sandwich-type results
Liu-Owa integral operator
Article.12.pdf
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[1]
R. M. Ali, V. Ravichandran, N. Seenivasagan, Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions, Bull. Malays. Math. Sci. Soc., 31 (2008), 193-207
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R. M. Ali, V. Ravichandran, N. Seenivasagan, Differential subordination and superordination of analytic functions defined by the multiplier transformation, Math. Inequal. Appl., 12 (2009), 123-139
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R. M. Ali, V. Ravichandran, N. Seenivasagan, Differential subordination and superordination of analytic functions defined by the Dziok-Srivastava linear operator , J. Franklin Inst., 347 (2010), 1762-1781
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R. M. Ali, V. Ravichandran, N. Seenivasagan, On subordination and superordination of the multiplier transformation for meromorphic functions, Bull. Malays. Math. Sci. Soc., 33 (2010), 311-324
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M. K. Aouf, T. Bulboacă, Subordination and superordination properties of multivalent functions defined by certain integral operator, J. Franklin Inst., 347 (2010), 641-653
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M. K. Aouf, T. M. Seoudy, Some preserving subordination and superordination of analytic functions involving the Liu- Owa integral operator, Comput. Math. Appl., 62 (2011), 3575-3580
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