scholarly journals Split equality common null point problem for Bregman quasi-nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3917-3932
Author(s):  
Ali Abkar ◽  
Elahe Shahrosvand
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Optimization Problem ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problem ◽  
Null Point ◽  
Point Problem ◽  
Reflexive Banach Spaces

In this paper, we introduce a new algorithm for solving the split equality common null point problem and the equality fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach spaces. We then apply this algorithm to the equality equilibrium problem and the split equality optimization problem. In this way, we improve and generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et al [11], and Sitthithakerngkiet et al [21].

scholarly journals The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuanheng Wang ◽  
Xiuping Wu ◽  
Chanjuan Pan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

AbstractIn this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

Iteration process for solving a fixed point problem of nonexpansive mappings in Banach spaces

2018 ◽  
Vol 29 (5-6) ◽  
pp. 783-792
Author(s):  
Sirintra Khoonyang ◽  
Mintra Inta ◽  
Prasit Cholamjiak
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Fixed Point Problem ◽  
Point Problem

An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

2018 ◽  
Vol 9 (3) ◽  
pp. 167-184 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Ferdinard Udochukwu Ogbuisi ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Monotone Operators ◽  
Convergence Result ◽  
Reflexive Banach Spaces ◽  
Strongly Monotone Operators ◽  
System Of Equilibrium Problems

Abstract In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.

scholarly journals Strong Convergence Theorems for Split Common Fixed Point Problem of Bregman Generalized Asymptotically Nonexpansive Mappings in Banach Spaces

2019 ◽  
pp. 35-50
Author(s):  
Yusuf Ibrahim
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

In this paper, a new iterative scheme is introduced and also strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented. The results are proved without the assumption of semicompactness property and or Opial condition

scholarly journals Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 722 ◽  
Author(s):  
Mujahid Abbas ◽  
Yusuf Ibrahim ◽  
Abdul Rahim Khan ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of left Bregman, strongly asymptotically non-expansive mappings in uniformly convex and uniformly smooth Banach spaces. A strong convergence theorem for the above problems are established. As an application, we solve a generalized mixed equilibrium problem, split Hammerstein integral equations, and a fixed-point problem, and provide a numerical example to support better findings of our result.

scholarly journals Strong convergence for monotone bilevel equilibria with constraints of variational inequalities and fixed points using subgradient extragradient implicit rule

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Long He ◽  
Yun-Ling Cui ◽  
Lu-Chuan Ceng ◽  
Tu-Yan Zhao ◽  
Dan-Qiong Wang ◽  
...  
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Implicit Rule

AbstractIn a real Hilbert space, let GSVI and CFPP represent a general system of variational inequalities and a common fixed point problem of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, via a new subgradient extragradient implicit rule, we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP constraints, i.e., a strongly monotone equilibrium problem over the common solution set of another monotone equilibrium problem, the GSVI and the CFPP. Some strong convergence results for the proposed algorithms are established under the mild assumptions, and they are also applied for finding a common solution of the GSVI, VIP, and FPP, where the VIP and FPP stand for a variational inequality problem and a fixed point problem, respectively.

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