Krasnoselski–mann Iteration for Hierarchical Fixed Points and Equilibrium Problem

Marino, Giuseppe; Colao, Vittorio; Muglia, Luigi; Yao, Yonghong

doi:10.1017/s000497270800107x

Cited by 15 publications

(4 citation statements)

References 27 publications

(25 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2009, Marino et al [21] introduced an iterative method to find common solutions of the following system of equilibrium problem and hierarchical fixed point problem:…”

Section: Introductionmentioning

confidence: 99%

Modified Krasnoselski–Mann iterative method for hierarchical fixed point problem and split mixed equilibrium problem

Kim

Majee

2020

J Inequal Appl

View full text Add to dashboard Cite

In this paper, we introduce a modified Krasnoselski–Mann type iterative method for capturing a common solution of a split mixed equilibrium problem and a hierarchical fixed point problem of a finite collection of k-strictly pseudocontractive nonself-mappings. Many of the algorithms for solving the split mixed equilibrium problem involve a step size which depends on the norm of a bounded linear operator. Since the computation of the operator norm is very difficult, we formulate our iterative algorithm in such a way that the implementation of the proposed algorithm does not require any prior knowledge of operator norm. Weak convergence results are established under mild conditions. We also establish strong convergence results for a certain class of hierarchical fixed point and split equilibrium problem. Our results generalize some important results in the recent literature.

show abstract

“…In 2009, Marino et al [21] introduced an iterative method to find common solutions of the following system of equilibrium problem and hierarchical fixed point problem:…”

Section: Introductionmentioning

confidence: 99%

Modified Krasnoselski–Mann iterative method for hierarchical fixed point problem and split mixed equilibrium problem

Kim

Majee

2020

J Inequal Appl

View full text Add to dashboard Cite

show abstract

“…We use V I(C, A) to denote the set of solutions of the variational inequality (1.1). On the other hand, a hierarchical fixed point problems [13][14][15][16][17][18][19][20] is the problem of finding a point…”

Section: Introductionmentioning

confidence: 99%

Some Existence and Convergence Theorems for Solving a System of Hierarchical Optimization Problems

Wairojjana

2016

Comput Math Model

View full text Add to dashboard Cite

In this article, we prove the existence and convergence theorems of the solution for a system of hierarchical variational inequality problem in Hilbert spaces. In this paper, we use Maingé's approach for finding a solution of the system of hierarchical variational inequality problems. Our result in this article improves, extends, and generalizes some well-known corresponding results in the literature.

show abstract

“…On the other hand, a hierarchical fixed point problem [4][5][6][7][8][9][10][11] is the problem of finding a point * ∈ ( ) such that ⟨ * , − * ⟩ ≥ 0, ∀ ∈ ( ) .…”

Section: Introductionmentioning

confidence: 99%

Existence and Algorithm for the Systems of Hierarchical Variational Inclusion Problems

Wairojjana

2014

Abstract and Applied Analysis

View full text Add to dashboard Cite

show abstract

Krasnoselski–mann Iteration for Hierarchical Fixed Points and Equilibrium Problem

Abstract: We give an explicit Krasnoselski-Mann type method for finding common solutions of the following system of equilibrium and hierarchical fixed points:

Cited by 15 publications

References 27 publications

Modified Krasnoselski–Mann iterative method for hierarchical fixed point problem and split mixed equilibrium problem

Modified Krasnoselski–Mann iterative method for hierarchical fixed point problem and split mixed equilibrium problem

Some Existence and Convergence Theorems for Solving a System of Hierarchical Optimization Problems

Existence and Algorithm for the Systems of Hierarchical Variational Inclusion Problems

Contact Info

Product

Resources

About