Approximate selections, fixed points, almost fixed points of multivalued mappings and generalized quasi-variational inequalities in -spaces

1999 ◽  
Vol 38 (2) ◽  
pp. 249-258 ◽  
Author(s):  
Xian Wu ◽  
Xianzhi Yuan
Keyword(s):  
Variational Inequalities ◽  
Fixed Points ◽  
Multivalued Mappings

scholarly journals On solving variational inequalities defined on fixed point sets of multivalued mappings in Banach spaces

2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Hong-Kun Xu ◽  
Luigi Muglia
Keyword(s):  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Multivalued Mappings ◽  
Multivalued Nonexpansive Mapping ◽  
Weakly Continuous ◽  
Duality Map ◽  
Implicit And Explicit ◽  
Essential Assumption

AbstractWe are concerned with the problem of solving variational inequalities which are defined on the set of fixed points of a multivalued nonexpansive mapping in a reflexive Banach space. Both implicit and explicit approaches are studied. Strong convergence of the implicit method is proved if the space satisfies Opial’s condition and has a duality map weakly continuous at zero, and the strong convergence of the explicit method is proved if the space has a weakly continuous duality map. An essential assumption on the multivalued nonexpansive mapping is that the mapping be single valued on its nonempty set of fixed points.

scholarly journals Fixed Points for Multivalued Mappings and the Metric Completeness

2009 ◽  
Vol 2009 (1) ◽  
pp. 972395 ◽  
Author(s):  
S Dhompongsa ◽  
H Yingtaweesittikul
Keyword(s):  
Fixed Points ◽  
Multivalued Mappings

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

scholarly journals An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

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