CQ method for generalized mixed equilibrium problem and fixed point problem of infinite family of quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces

2011 ◽  
Vol 30 (4) ◽  
pp. 931-942
Author(s):  
Min Liu
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Asymptotically Nonexpansive ◽  
Cq Method ◽  
Generalized Mixed Equilibrium

On split generalized mixed equilibrium and fixed point problems of an infinite family of quasi-nonexpansive multi-valued mappings in real Hilbert spaces

2021 ◽  
pp. 2250082
Author(s):  
F. Akutsah ◽  
H. A. Abass ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Infinite Family ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

In this paper, we study split generalized mixed equilibrium problem and fixed point problem in real Hilbert spaces with a view to analyze an iterative method for approximating a common solution of split generalized mixed equilibrium problem and fixed point problem of an infinite family of a quasi-nonexpansive multi-valued mappings. The iterative algorithm introduced in this paper is designed in such a way that it does not require the knowledge of the operator norm. We state and prove a strong convergence result of the aforementioned problems and also give application of our main result to split variational inequality problem. Our result complements and extends some related results in literature.

scholarly journals Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Pongrus Phuangphoo ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Dual Space ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Existence Of A Solution ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We study and establish the existence of a solution for a generalized mixed equilibrium problem with a bifunction defined on the dual space of a Banach space. Furthermore, we also modify Halpern-Mann iterations for finding a common solution of a generalized mixed equilibrium problem and a fixed point problem. Under suitable conditions of the purposed iterative sequences, the strong convergence theorems are established by using sunny generalized nonexpansive retraction in Banach spaces. Our results extend and improve various results existing in the current literature.

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 A Unified Algorithm for Solving Split Generalized Mixed Equilibrium Problem, and for Finding Fixed Point of Nonspreading Mapping in Hilbert Spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 211-232 ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Kazeem Olawale Oyewole ◽  
Chibueze Christian Okeke ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Common Solution ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

Abstract The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces.We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.

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.

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