A new hybrid method for hierarchical fixed points problems and variational inequality problems

Optimization ◽  
2011 ◽  
Vol 60 (6) ◽  
pp. 685-696
Author(s):  
Yeong-Cheng Liou
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Hybrid Method ◽  
Variational Inequality Problems

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.

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