A Strong Convergence Theorem by the Shrinking Projection Method for the Split Common Null Point Problem in Banach Spaces

2016 ◽  
Vol 37 (5) ◽  
pp. 541-553 ◽  
Author(s):  
Mayumi Hojo ◽  
Wataru Takahashi
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Projection Method ◽  
Convergence Theorem ◽  
Null Point ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Shrinking Projection Method

scholarly journals Convergence theorems for finding the split common null point in Banach spaces

2017 ◽  
Vol 18 (2) ◽  
pp. 345 ◽  
Author(s):  
Suthep Suantai ◽  
Kittipong Srisap ◽  
Natthapong Naprang ◽  
Manatsawin Mamat ◽  
Vithoon Yundon ◽  
...  
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Null Point ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Convergence Theorems ◽  
Numerical Examples

<p>In this paper, we introduce a new iterative scheme for solving the split common null point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.</p>

scholarly journals A Strong Convergence Theorem for Relatively Nonexpansive Mappings and Equilibrium Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mei Yuan ◽  
Xi Li ◽  
Xue-song Li ◽  
John J. Liu
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Projection Method ◽  
Convergence Theorem ◽  
Projection Operator ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

Relatively nonexpansive mappings and equilibrium problems are considered based on a shrinking projection method. Using properties of the generalizedf-projection operator, a strong convergence theorem for relatively nonexpansive mappings and equilibrium problems is proved in Banach spaces under some suitable conditions.

scholarly journals Convex Minimization with Constraints of Systems of Variational Inequalities, Mixed Equilibrium, Variational Inequality, and Fixed Point Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-28
Author(s):  
Lu-Chuan Ceng ◽  
Cheng-Wen Liao ◽  
Chin-Tzong Pang ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Projection Method ◽  
Real Hilbert Space ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Shrinking Projection Method ◽  
Mixed Equilibrium

We introduce and analyze one iterative algorithm by hybrid shrinking projection method for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: finitely many generalized mixed equilibrium problems, finitely many variational inequalities, the general system of variational inequalities and the fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm by hybrid shrinking projection method for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.

A shrinking projection method for solving the split common null point problem in Banach spaces

2018 ◽  
Vol 81 (3) ◽  
pp. 813-832 ◽  
Author(s):  
Truong Minh Tuyen ◽  
Nguyen Song Ha ◽  
Nguyen Thi Thu Thuy
Keyword(s):  
Banach Spaces ◽  
Projection Method ◽  
Null Point ◽  
Point Problem ◽  
Shrinking Projection Method

SHRINKING PROJECTION ALGORITHMS FOR THE SPLIT COMMON NULL POINT PROBLEM

2017 ◽  
Vol 96 (2) ◽  
pp. 299-306 ◽  
Author(s):  
VAHID DADASHI
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Convergence Theorem ◽  
Maximal Monotone ◽  
Null Point ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Projection Algorithms

We consider the split common null point problem in Hilbert space. We introduce and study a shrinking projection method for finding a solution using the resolvent of a maximal monotone operator and prove a strong convergence theorem for the algorithm.

An iterative algorithm with inertial technique for solving the split common null point problem in Banach spaces

2021 ◽  
pp. 2250120
Author(s):  
Yan Tang ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Banach Spaces ◽  
Split Feasibility Problem ◽  
Null Point ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Inertial Algorithm ◽  
The Split Feasibility Problem ◽  
Inertial Technique ◽  
Split Feasibility

In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.

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