scholarly journals Stability and Convergence Analysis for Set-Valued Extended Generalized Nonlinear Mixed Variational Inequality Problems and Generalized Resolvent Dynamical Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Iqbal Ahmad ◽  
Zahoor Ahmad Rather ◽  
Rais Ahmad ◽  
Ching-Feng Wen
Keyword(s):  
Dynamical System ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Variational Inequality Problem ◽  
Stability And Convergence ◽  
Mixed Variational Inequality ◽  
Generalized Resolvent ◽  
Inequality Problem ◽  
System A ◽  
Type Algorithm

In this paper, we study a set-valued extended generalized nonlinear mixed variational inequality problem and its generalized resolvent dynamical system. A three-step iterative algorithm is constructed for solving set-valued extended generalized nonlinear variational inequality problem. Convergence and stability analysis are also discussed. We have shown the globally exponential convergence of generalized resolvent dynamical system to a unique solution of set-valued extended generalized nonlinear mixed variational inequality problem. In support of our main result, we provide a numerical example with convergence graphs and computation tables. For illustration, a comparison of our three-step iterative algorithm with Ishikawa-type algorithm and Mann-type algorithm is shown.

scholarly journals An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Mohammad Farid ◽  
Rehan Ali ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Field Of Study ◽  
Inequality Problem ◽  
Numerical Example ◽  
Common Solution ◽  
Generalized Equilibrium ◽  
The Common

In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. Furthermore, we list some consequences of our established algorithm. Finally, we construct a numerical example to demonstrate the applicability of the theorem. We emphasize that the result accounted in the manuscript unifies and extends various results in this field of study.

scholarly journals A New System of Multivalued Mixed Variational Inequality Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xi Li ◽  
Xue-song Li
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Projection Algorithm ◽  
Mixed Variational Inequality ◽  
Inequality Problem ◽  
Special Cases ◽  
Systems Of Variational Inequalities ◽  
Special Case ◽  
New System

We consider a new system of multivalued mixed variational inequality problem, which includes some known systems of variational inequalities as special cases. Under suitable conditions, the existence of solutions for the system of multivalued mixed variational inequality problem and the convergence of iterative sequences generated by the generalizedf-projection algorithm are proved. A perturbational algorithm for solving a special case of multivalued mixed variational inequality problem is formally constructed. The results concerned with the existence of solutions and the convergence of iterative sequences generated by the perturbational algorithm are also given. Some known results are improved and generalized.

scholarly journals On completely generalized multi-valued co-variational inequalities involving strongly accretive operators

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 657-663
Author(s):  
Rais Ahmad ◽  
Syed Irfan
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Accretive Operators ◽  
Inequality Problem

In this paper we consider the completely generalized multi-valued co-variational inequality problem in Banach spaces and construct an iterative algorithm. We prove the existence of solutions for our problem involving strongly accretive operators and convergence of iterative sequences generated by the algorithm.

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