Convergence theorems for a finite family of generalized nonexpansive multivalued mappings in CAT(0) spaces

In this paper, we are concerned with the split equality problem of finding an element in the zero point set of the sum of two monotone operators and in the common fixed point set of a finite family of quasi-nonexpansive set-valued mappings. Strong convergence theorems are established under suitable condition in an infinite dimensional Hilbert spaces. Some applications of the main results are also provided.

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“…The proof of the following result is similar to the proof of Theorem 3.4 in [29], and so is not included.…”

Section: Preliminariesmentioning

confidence: 99%

Split equality monotone variational inclusions and fixed point problem of set-valued operator

Eslamian

Fakhri

2017

Acta Universitatis Sapientiae, Mathematica

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“…Now we define the multivalued version of the condition ( E ) and in the following way (see Abkar and Eslamain 2012 ).…”

Section: Preliminariesmentioning

confidence: 99%

“…Recently, Abkar and Eslamain ( 2012 ) introduced an iterative process for a finite family of generalized nonexpansive multivalued mappings and proved -convergence and strong convergence theorems in CAT(0) spaces.…”

Section: Introductionmentioning

confidence: 99%

“…In the view of the fact, many researchers motivated towards to introduced various numbers of iterative processes for approximating fixed points and established convergence and strong convergence theorems, not only for multivalued nonexpansve mappings but also its general class of multivalued mappings in CAT(0) spaces (see Abkar and Eslamain 2012 ; Dhompongsa et al. 2012 ; Eslamian and Abkar 2011 ; Khan et al.…”

Section: Introductionmentioning

confidence: 99%

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Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces

et al. 2016

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In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some -convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535–540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature.

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“…The theory of set-valued mappings has applications in control theory, convex optimization, differential equations and economics. Fixed point theory for set-valued mappings has been studied by many authors, see [1,2,11,12,14,19,22,23,32] and the references therein. In the resent years, iterative algorithms for finding a common element of a set of solutions of equilibrium problem and the set of fixed points of nonexpansive mappings in a real Hilbert space have been studied by many authors (see, e.g., [3,4,5,7,8,9,29,30,31,33,35,36,37]).…”

Section: Introductionmentioning

confidence: 99%

A new general algorithm for set-valued mappings and equilibrium problem

Vahidi¹

2016

J. Nonlinear Sci. Appl.

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We consider a multi-step algorithm to approximate a common element of the set of solutions of monotone and Lipschitz-type continuous equilibrium problems, and the set of common fixed points of a finite family of set-valued mappings satisfying condition (E). We prove strong convergence theorems of such an iterative scheme in real Hilbert spaces. This common solution is the unique solution of a variational inequality problem and it satisfies the optimality condition for a minimization problem. The main result extends various results exiting in the literature.

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Convergence theorems for a finite family of generalized nonexpansive multivalued mappings in CAT(0) spaces

Cited by 16 publications

References 15 publications

Split equality monotone variational inclusions and fixed point problem of set-valued operator

Split equality monotone variational inclusions and fixed point problem of set-valued operator

Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces

A new general algorithm for set-valued mappings and equilibrium problem

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