scholarly journals Construction of a common solution of a finite family of variational inequality problems for monotone mappings

2016 ◽  
Vol 09 (04) ◽  
pp. 1645-1657
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Variational Inequality ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Monotone Mappings ◽  
Common Solution

scholarly journals Viscosity Approximation Methods with Errors and Strong Convergence Theorems for a Common Point of Pseudocontractive and Monotone Mappings: Solutions of Variational Inequality Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yan Tang
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Iterative Algorithms ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Monotone Mappings ◽  
Convergence Theorems ◽  
Common Solution ◽  
The Common ◽  
Viscosity Approximation Methods

We introduce two proximal iterative algorithms with errors which converge strongly to the common solution of certain variational inequality problems for a finite family of pseudocontractive mappings and a finite family of monotone mappings. The strong convergence theorems are obtained under some mild conditions. Our theorems extend and unify some of the results that have been proposed for this class of nonlinear mappings.

scholarly journals On a Viscosity Iterative Method for Solving Variational Inequality Problems in Hadamard Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 143
Author(s):  
Kazeem Olalekan Aremu ◽  
Chinedu Izuchukwu ◽  
Hammed Anuolwupo Abass ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Variational Inequality ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Monotone Mappings ◽  
Hadamard Space ◽  
Common Solution ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings ◽  
Demicontractive Mappings ◽  
Viscosity Iterative Method

In this paper, we propose and study an iterative algorithm that comprises of a finite family of inverse strongly monotone mappings and a finite family of Lipschitz demicontractive mappings in an Hadamard space. We establish that the proposed algorithm converges strongly to a common solution of a finite family of variational inequality problems, which is also a common fixed point of the demicontractive mappings. Furthermore, we provide a numerical experiment to demonstrate the applicability of our results. Our results generalize some recent results in literature.

scholarly journals A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Pongrus Phuangphoo ◽  
Poom Kumam
Keyword(s):  
Variational Inequality ◽  
Iterative Procedure ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Projection Algorithm ◽  
Common Solution ◽  
The Common ◽  
System Of Equilibrium Problems

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-ϕ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.

scholarly journals A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 248 ◽  
Author(s):  
Suthep Suantai ◽  
Pronpat Peeyada ◽  
Damrongsak Yambangwai ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Infinite Dimensional ◽  
Common Solution ◽  
Line Method ◽  
The Common ◽  
Monotone Hybrid Algorithm

In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

scholarly journals An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Wanna Sriprad ◽  
Somnuk Srisawat
Keyword(s):  
Variational Inequality ◽  
Real Hilbert Space ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Variational Inclusion ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Convex Minimization Problems

The purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. In addition, by using our result, we obtain some additional results involving split convex minimization problems (SCMPs) and split feasibility problems (SFPs). Also, we give some numerical examples for supporting our main theorem.

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