System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

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Coincidence and invariant approximation theorems for generalizedf-nonexpansive multivalued mappings

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms/2006/17637 ◽

2006 ◽

Vol 2006 ◽

pp. 1-18 ◽

Cited By ~ 2

Author(s):

A. R. Khan ◽

F. Akbar ◽

N. Sultana ◽

N. Hussain

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Substantial Improvement ◽

Multivalued Mappings ◽

Random Coincidence ◽

Approximation Theorems ◽

Invariant Approximation ◽

Point Invariant ◽

Common Fixed Point Theorems

The main purpose of this paper is to prove some new coincidence and common fixed point theorems for noncommuting generalizedf-nonexpansive multivalued mappings on non-starshaped domain in the framework of a Banach space. As applications, related common fixed point, invariant approximation, and random coincidence point results are established. This work provides extension as well as substantial improvement of several results in the existing literature.

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

Canadian Mathematical Bulletin ◽

10.4153/cmb-2015-029-x ◽

2016 ◽

Vol 59 (01) ◽

pp. 3-12 ◽

Cited By ~ 2

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.

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Some related fixed point theorems for multivalued mappings on two metric spaces

Carpathian Mathematical Publications ◽

10.15330/cmp.12.2.392-400 ◽

2020 ◽

Vol 12 (2) ◽

pp. 392-400

Author(s):

Ö. Biçer ◽

M. Olgun ◽

T. Alyildiz ◽

I. Altun

Keyword(s):

Fixed Point ◽

Classical Result ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Multivalued Mappings ◽

Compact Set ◽

Complete Metric Spaces ◽

Bounded Set ◽

Contraction Type ◽

Definition Of

The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via $F$-contraction type conditions.

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