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.

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.

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 Fixed Points of Eventually Δ-Restrictive and Δ(ϵ)-Restrictive Set-Valued Maps in Metric Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 127 ◽  
Author(s):  
Pradip Debnath ◽  
Manuel de La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Intrinsic Property ◽  
Point Theory ◽  
Symmetry Principles ◽  
Definition Of ◽  
Metric Function

The symmetry concept is an intrinsic property of metric spaces as the metric function generalizes the notion of distance between two points. There are several remarkable results in science in connection with symmetry principles that can be proved using fixed point arguments. Therefore, fixed point theory and symmetry principles bear significant correlation between them. In this paper, we introduce the new definition of the eventually Δ -restrictive set-valued map together with the concept of p-orbital continuity. Further, we introduce another new concept called the Δ ( ϵ ) -restrictive set-valued map. We establish several fixed point results related to these maps and proofs of these results also provide us with schemes to find a fixed point. In a couple of results, the stronger condition of compactness of the underlying metric space is assumed. Some results are illustrated with examples.

scholarly journals Fixed points of Lie group actions on surfaces

1986 ◽  
Vol 6 (1) ◽  
pp. 149-161 ◽  
Author(s):  
J. F. Plante
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Lie Groups ◽  
Euler Characteristic ◽  
Lie Group ◽  
Stationary Point ◽  
Compact Surface ◽  
The Other ◽  
Continuous Action ◽  
Finite Dimensional

AbstractLetGbe a connected finite-dimensional Lie group andMa compact surface. We investigate whether, for a givenGandM, every continuous action ofGonMmust have a fixed (stationary) point. It is shown that whenGis nilpotent andMhas non-zero Euler characteristic that every action ofGonMmust have a fixed point. On the other hand, it is shown that the non-abelian 2-dimensional Lie group (affine group of the line) acts without fixed points on every compact surface. These results make it possible to complete this investigation for Lie groups of dimension at most 3.

scholarly journals The non-SUSY AdS6 and AdS7 fixed points are brane-jet unstable

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Minwoo Suh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Decay Channel ◽  
Scalar Potential ◽  
The Other ◽  
Other Hand ◽  
Weak Gravity

Abstract In six- and seven-dimensional gauged supergravity, each scalar potential has one supersymmetric and one non-supersymmetric fixed points. The non-supersymmetric AdS7 fixed point is perturbatively unstable. On the other hand, the non-supersymmetric AdS6 fixed point is known to be perturbatively stable. In this note we examine the newly proposed non-perturbative decay channel, called brane-jet instabilities of the AdS6 and AdS7 vacua. We find that when they are uplifted to massive type IIA and eleven- dimensional supergravity, respectively, the non-supersymmetric AdS6 and AdS7 vacua are both brane-jet unstable, in fond of the weak gravity conjecture.

scholarly journals (C , Ψ * , G ) Class of Contractions and Fixed Points in a Metric Space Endowed with a Graph

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 482 ◽  
Author(s):  
Reny George ◽  
Ekta Tamrakar ◽  
Jelena Vujaković ◽  
Hemant Pathak ◽  
Selvavinayagam Velusamy
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Admissible Set ◽  
Contraction Mappings ◽  
Control Functions ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space.

scholarly journals Fixed Points of Some Asymptotically Regular Multivalued Mappings Satisfying a Kannan-Type Condition

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 24
Author(s):  
Pradip Debnath ◽  
Zoran D. Mitrović ◽  
Hari Mohan Srivastava
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Type Condition ◽  
Asymptotically Regular

In this paper, we establish some existence of fixed-point results for some asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness of the underlying metric space or continuity of the mapping.

scholarly journals Theorems on Fixed Points for Asymptotically Regular Sequences and Maps in

2017 ◽  
Vol 22 (1) ◽  
pp. 48
Author(s):  
Mohammad S. Khan ◽  
Pankaj K. Jhade
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Regular Sequences ◽  
Regular Maps ◽  
Asymptotically Regular

In this paper, we present some fixed point theorems for asymptotically regular sequences and asymptotically regular maps in complete

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

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