scholarly journals A Cyclic Method for Solutions of a Class of Split Variational Inequality Problem in Banach Space

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Bashir Ali ◽  
Aisha A. Adam ◽  
Yusuf Ibrahim
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Variational Inequality Problem ◽  
Strong Convergence Theorem ◽  
Inequality Problem ◽  
Cyclic Algorithm ◽  
Split Variational Inequality ◽  
Split Variational Inequality Problem

In this paper, a cyclic algorithm for approximating a class of split variational inequality problem is introduced and studied in some Banach spaces. A strong convergence theorem is proved. Some applications of the theorem are presented. The results presented here improve, unify, and generalize certain recent results in the literature.

scholarly journals Algorithms for Solving the Variational Inequality Problem over the Triple Hierarchical Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Thanyarat Jitpeera ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Variational Inequality Problem ◽  
Strong Convergence Theorem ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Point Set ◽  
Monotone Variational Inequality

This paper discusses the monotone variational inequality over the solution set of the variational inequality problem and the fixed point set of a nonexpansive mapping. The strong convergence theorem for the proposed algorithm to the solution is guaranteed under some suitable assumptions.

scholarly journals Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 379 ◽  
Author(s):  
Chanjuan Pan ◽  
Yuanheng Wang
Keyword(s):  
Variational Inequality ◽  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Equilibrium Problems ◽  
Variational Inequality Problem ◽  
Zero Point ◽  
Strong Convergence Theorem ◽  
Implicit Iterative Method

In this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreover, we provide some applications to zero-point problems and equilibrium problems. Further, a numerical example is given to illustrate our convergence analysis. The results generalize and improve corresponding results in the literature.

scholarly journals A Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces

2021 ◽  
Vol 53 ◽  
Author(s):  
Wongvisarut Khuangsatung ◽  
Atid Kangtunyakarn
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Contractive Mapping ◽  
Smooth Banach Space ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Inequality Problem ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.

Convergence analysis of an inertial accelerated iterative algorithm for solving split variational inequality problem

2019 ◽  
Vol 10 (4) ◽  
pp. 339-353 ◽  
Author(s):  
Ferdinard U. Ogbuisi ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Operator Norm ◽  
Step Size ◽  
Inequality Problem ◽  
Convex Minimization Problems ◽  
Split Variational Inequality ◽  
Split Variational Inequality Problem

AbstractIn this paper, we introduce an iterative scheme involving an inertial term and a step size independent of the operator norm for approximating a solution to a split variational inequality problem in a real Hilbert space. Furthermore, we prove a convergence theorem for the sequence generated by the proposed operator norm independent inertial accelerated iterative scheme. We applied our result to solve split convex minimization problems, split zero problem and further give a numerical example to demonstrate the efficiency of the proposed algorithm.

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