Modified Krasnoselski–Mann type iterative algorithm with strong convergence for hierarchical fixed point problem and split monotone variational inclusions

2021 ◽  
Vol 393 ◽  
pp. 113501
Author(s):  
Dao-Jun Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Variational Inclusions ◽  
Hierarchical Fixed Point Problem ◽  
Hierarchical Fixed Point

Solving split equality common fixed point problem for infinite families of demicontractive mappings

2018 ◽  
Vol 34 (3) ◽  
pp. 321-331
Author(s):  
ADISAK HANJING ◽  
◽  
SUTHEP SUANTAI ◽  
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Demicontractive Mappings

In this paper, we consider the split equality common fixed point problem of infinite families of demicontractive mappings in Hilbert spaces. We introduce a simultaneous iterative algorithm for solving the split equality common fixed point problem of infinite families of demicontractive mappings and prove a strong convergence of the proposed algorithm under some control conditions.

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 Algorithms for Solving System of Extended General Variational Inclusions and Fixed Points Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-27
Author(s):  
Narin Petrot ◽  
Javad Balooee
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Variational Inclusions ◽  
Lipschitzian Mapping ◽  
Existence And Uniqueness Theorem ◽  
Equivalent Formulation ◽  
Nonlinear Operators ◽  
Uniformly Lipschitzian Mapping

We introduce a new system of extended general nonlinear variational inclusions with different nonlinear operators and establish the equivalence between the aforesaid system and the fixed point problem. By using this equivalent formulation, we prove the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions. We suggest and analyze a new resolvent iterative algorithm to approximate the unique solution of the system of extended general nonlinear variational inclusions which is a fixed point of a nearly uniformly Lipschitzian mapping. Subsequently, the convergence analysis of the proposed iterative algorithm under some suitable conditions is considered. Furthermore, some related works to our main problem are pointed out and discussed.

Sign in / Sign up

Export Citation Format

Share Document