scholarly journals System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 5
Author(s):  
Lu-Chuan Ceng ◽  
Mihai Postolache ◽  
Xiaolong Qin ◽  
Yonghong Yao
Keyword(s):  
Banach Spaces ◽  
Infinite Family ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Variational Inclusions ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Mild Conditions ◽  
Pseudocontractive Mappings

The purpose of this paper is to solve the general system of variational inclusions (GSVI) with hierarchical variational inequality (HVI) constraint, for an infinite family of continuous pseudocontractive mappings in Banach spaces. By utilizing the equivalence between the GSVI and the fixed point problem, we construct an implicit multiple-viscosity approximation method for solving the GSVI. Under very mild conditions, we prove the strong convergence of the proposed method to a solution of the GSVI with the HVI constraint, for infinitely many pseudocontractions.

scholarly journals Systems of Variational Inequalities with Nonlinear Operators

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 338 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
General System ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings ◽  
Common Fixed Point Problem

In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces.

scholarly journals Split equality common null point problem for Bregman quasi-nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3917-3932
Author(s):  
Ali Abkar ◽  
Elahe Shahrosvand
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Optimization Problem ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problem ◽  
Null Point ◽  
Point Problem ◽  
Reflexive Banach Spaces

In this paper, we introduce a new algorithm for solving the split equality common null point problem and the equality fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach spaces. We then apply this algorithm to the equality equilibrium problem and the split equality optimization problem. In this way, we improve and generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et al [11], and Sitthithakerngkiet et al [21].

scholarly journals Viscosity approximation method for solving variational inequality problem in real Banach spaces

2021 ◽  
pp. 1-20
Author(s):  
Godwin Ugwunnadi
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Approximation Method ◽  
Variational Inequality Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Inequality Problem ◽  
Mild Conditions ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.

scholarly journals Iterations for systems of variational inequalities, fixed points of pseudocontractions and zeros of accretive operators

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4769-4784
Author(s):  
Lu-Chuan Ceng ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
General System ◽  
Accretive Operator ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Accretive Operators ◽  
Common Solution ◽  
Pseudocontractive Mappings ◽  
Systems Of Variational Inequalities

In this paper, we introduce implicit composite three-step Mann iterations for finding a common solution of a general system of variational inequalities, a fixed point problem of a countable family of pseudocontractive mappings and a zero problem of an accretive operator in Banach spaces. Strong convergence of the suggested iterations are given.

scholarly journals On a General Extragradient Implicit Method and Its Applications to Optimization

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 124
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Extragradient Method ◽  
General System ◽  
Zero Point ◽  
Fixed Point Problem ◽  
Implicit Method ◽  
Point Problem ◽  
Viscosity Approximation ◽  
Uniformly Smooth ◽  
Common Fixed Point Problem ◽  
Mann’S Iteration

Let X be a Banach space with both q-uniformly smooth and uniformly convex structures. This article introduces and considers a general extragradient implicit method for solving a general system of variational inequalities (GSVI) with the constraints of a common fixed point problem (CFPP) of a countable family of nonlinear mappings { S n } n = 0 ∞ and a monotone variational inclusion, zero-point, problem. Here, the constraints are symmetrical and the general extragradient implicit method is based on Korpelevich’s extragradient method, implicit viscosity approximation method, Mann’s iteration method, and the W-mappings constructed by { S n } n = 0 ∞ .

scholarly journals The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuanheng Wang ◽  
Xiuping Wu ◽  
Chanjuan Pan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

AbstractIn this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

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