scholarly journals Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Fixed Points ◽  
Tangent Cone ◽  
Compact Set ◽  
Set Valued Mapping ◽  
Clarke Tangent Cone ◽  
Set Valued Mappings ◽  
Existence Of Equilibria

We prove a new result of existence of equilibria for an u.s.c. set-valued mappingFon a compact setSofRnwhich is epi-Lipschitz and satisfies a weak tangential condition. Equivalently this provides existence of fixed points of the set-valued mappingx⇉F(x)-x. The main point of our result lies in the fact that we do not impose the usual tangential condition in terms of the Clarke tangent cone. Illustrative examples are stated showing the importance of our results and that the existence of such equilibria does not need necessarily such usual tangential condition.

scholarly journals Approximating Fixed Points of The General Asymptotic Set Valued Mappings

2020 ◽  
Vol 18 ◽  
pp. 52-59
Author(s):  
Salwa Salman Abed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Reflexive Banach Spaces ◽  
Set Valued Mapping ◽  
Set Valued Mappings ◽  
Fixed Point Iterative Method

  The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping  and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by  yn+1 = tn z+ (1-tn )un ,  un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces.  As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

A Characterization of Proximal Subgradient Set-Valued Mappings

1993 ◽  
Vol 36 (1) ◽  
pp. 116-122 ◽  
Author(s):  
R. A. Poliquin
Keyword(s):  
Lower Semicontinuous ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Set Valued Mapping ◽  
Selection Property ◽  
Set Valued Mappings ◽  
Bounded Below

AbstractIn this paper we tackle the problem of identifying set-valued mappings that are subgradient set-valued mappings. We show that a set-valued mapping is the proximal subgradient mapping of a lower semicontinuous function bounded below by a quadratic if and only if it satisfies a monotone selection property.

scholarly journals Related fixed points for set-valued mappings on two uniform spaces

2004 ◽  
Vol 2004 (69) ◽  
pp. 3783-3791 ◽  
Author(s):  
Duran Türkoğlu ◽  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Uniform Spaces ◽  
Set Valued Mappings

Some related fixed point theorems for set-valued mappings on two complete and compact uniform spaces are proved.

scholarly journals EXISTENCE OF FIXED POINTS OF SET-VALUED MAPPINGS IN b-METRIC SPACES

2016 ◽  
Vol 32 (3) ◽  
pp. 319-332 ◽  
Author(s):  
Hojjat Afshari ◽  
Hassen Aydi ◽  
Erdal Karapinar
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Set Valued Mappings

scholarly journals Approximate fixed points of set-valued mapping in b-metric space

2016 ◽  
Vol 09 (06) ◽  
pp. 3760-3772 ◽  
Author(s):  
Bessem Samet ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Set Valued Mapping

scholarly journals Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 411
Author(s):  
Pradip Debnath ◽  
Manuel de La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
The Other ◽  
Broad Category ◽  
Set Valued Mappings ◽  
Metric Function ◽  
Asymptotically Regular

The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities.

Preliminaries from set-valued analysis

2012 ◽  
Author(s):  
Rafal Goebel ◽  
Ricardo G. Sanfelice ◽  
Andrew R. Teel
Keyword(s):  
Hybrid Systems ◽  
Differential Inclusions ◽  
Set Valued Mapping ◽  
Continuity Properties ◽  
Set Valued Mappings

This chapter includes the necessary background on further developments in the theory of hybrid systems. It first presents the notion of convergence for a sequence of sets and how it generalizes the notion of convergence of a sequence of points. The chapter then deals with set-valued mappings and their continuity properties. Given a set-valued mapping M : ℝᵐ ⇉ ℝⁿ, the chapter defines the range of M as the set rgeM = {‎y ∈ ℝⁿ : Ǝx ∈ ℝᵐ such that y ∈ M(x)}‎; and the graph of M as the set gphM = {‎(x,y) ∈ ℝᵐ × ℝⁿ : y ∈ M(x)}‎. The chapter also specializes some of the concepts, such as graphical convergence, to hybrid arcs and provides further details in such a setting. Finally, the chapter discusses differential inclusions.

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