scholarly journals Strong convergence algorithm for the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem

2021 ◽  
pp. 1-32
Author(s):  
Shamshad Husain ◽  
Mohd Asad ◽  
Mubashshir Uddin Khairoowala
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Common Element ◽  
Point Problem ◽  
Variational Inclusions ◽  
Generalized Equilibrium Problem ◽  
Solution Sets ◽  
Generalized Equilibrium ◽  
Split Generalized Equilibrium Problem

The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.

scholarly journals Approximation of common solutions for a fixed point problem of asymptotically nonexpansive mapping and a generalized equilibrium problem in Hilbert space

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Richard Osward ◽  
Santosh Kumar ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Equilibrium Problem ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Common Solution ◽  
Asymptotically Nonexpansive ◽  
Generalized Equilibrium

Abstract In this paper, we introduce an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequences generated by the iterative algorithm converge strongly to a common solution of the generalized equilibrium problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. Some applications of main results are also provided.

scholarly journals Iterative Scheme for Split Variational Inclusion and a Fixed-Point Problem of a Finite Collection of Nonexpansive Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
M. Dilshad ◽  
A. F. Aljohani ◽  
M. Akram
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Common Element ◽  
Finite Collection ◽  
Point Problem ◽  
Common Solution ◽  
The Common

This article is aimed at introducing an iterative scheme to approximate the common solution of split variational inclusion and a fixed-point problem of a finite collection of nonexpansive mappings. It is proven that under some suitable assumptions, the sequences achieved by the proposed iterative scheme converge strongly to a common element of the solution sets of these problems. Some consequences of the main theorem are also given. Finally, the convergence analysis of the sequences achieved from the iterative scheme is illustrated with the help of a numerical example.

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