scholarly journals Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2292
Author(s):  
Mujahid Abbas ◽  
Rizwan Anjum ◽  
Vasile Berinde
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Variational Inequality Problems ◽  
Iterative Approximation ◽  
Iteration Methods ◽  
Split Feasibility ◽  
Iteration Processes

The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

scholarly journals On Solutions of Variational Inequality Problems via Iterative Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Iterative Methods ◽  
Common Point ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Important Class ◽  
Pseudocontractive Mappings ◽  
Accretive Mappings ◽  
Nonlinear Mappings

We investigate an algorithm for a common point of fixed points of a finite family of Lipschitz pseudocontractive mappings and solutions of a finite family ofγ-inverse strongly accretive mappings. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings.

scholarly journals Variational inequality problems inH-spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-18
Author(s):  
Akrur Behera ◽  
Prasanta Kumar Das
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Complementarity Problem ◽  
Vector Variational Inequality ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Lefschetz Number ◽  
Topological Vector Spaces ◽  
Invex Set ◽  
Invex Function

The concept ofη-invex set is explored and the concept ofT-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended toH-spaces and differentiablen-manifolds. The solution of complementarity problem is also studied in the presence of fixed points or Lefschetz number.

scholarly journals Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Panisa Lohawech ◽  
Anchalee Kaewcharoen ◽  
Ali Farajzadeh
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Descent Method ◽  
Variational Inequality Problems ◽  
Steepest Descent Method ◽  
Split Feasibility Problems ◽  
The Common ◽  
Split Feasibility

In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms.

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