scholarly journals Hybrid steepest iterative algorithm for a hierarchical fixed point problem

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Shamshad Husain ◽  
Nisha Singh
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point

scholarly journals Iterative algorithms of common solutions for a hierarchical fixed point problem, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yali Zhao ◽  
Xin Liu ◽  
Ruonan Sun
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
System Of Variational Inequalities ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point

AbstractIn this paper, we suggest and analyze an iterative algorithm to approximate a common solution of a hierarchical fixed point problem for nonexpansive mappings, a system of variational inequalities, and a split equilibrium problem in Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence generated by the proposed iterative method converges strongly to a common element of the solution set of these three kinds of problems. The results obtained here extend and improve the corresponding results of the relevant literature.

scholarly journals Hybrid Viscosity Approaches to General Systems of Variational Inequalities with Hierarchical Fixed Point Problem Constraints in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-18
Author(s):  
Lu-Chuan Ceng ◽  
Saleh A. Al-Mezel ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Steepest Descent Method ◽  
Point Problem ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point

The purpose of this paper is to introduce and analyze hybrid viscosity methods for a general system of variational inequalities (GSVI) with hierarchical fixed point problem constraint in the setting of real uniformly convex and 2-uniformly smooth Banach spaces. Here, the hybrid viscosity methods are based on Korpelevich’s extragradient method, viscosity approximation method, and hybrid steepest-descent method. We propose and consider hybrid implicit and explicit viscosity iterative algorithms for solving the GSVI with hierarchical fixed point problem constraint not only for a nonexpansive mapping but also for a countable family of nonexpansive mappings inX, respectively. We derive some strong convergence theorems under appropriate conditions. Our results extend, improve, supplement, and develop the recent results announced by many authors.

scholarly journals An iterative scheme for split equality equilibrium problems and split equality hierarchical fixed point problem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Monairah Alansari
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Equilibrium Problem ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point ◽  
Weak Convergence Theorem

AbstractThis paper deals with a split equality equilibrium problem for pseudomonotone bifunctions and a split equality hierarchical fixed point problem for nonexpansive and quasinonexpansive mappings. We suggest and analyze an iterative scheme where the stepsizes do not depend on the operator norms, the so-called simultaneous projected subgradient-proximal iterative scheme for approximating a common solution of the split equality equilibrium problem and the split equality hierarchical fixed point problem. Further, we prove a weak convergence theorem for the sequences generated by this scheme. Furthermore, we discuss some consequences of the weak convergence theorem. We present a numerical example to justify the main result.

scholarly journals Hybrid viscosity approximation methods for systems of variational inequalities and hierarchical fixed point problems

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1927-1947
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
System Of Variational Inequalities ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point

In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities with a hierarchical fixed point problem constraint for an infinite family of nonexpansive mappings. We show that the proposed algorithms converge strongly to a solution of the general system of variational inequalities, which is a unique solution of the hierarchical fixed point problem.

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