Necessary Conditions and Sufficient Conditions for Finding a Common Fixed Point of a Family of Maps Using a Distributed Algorithm

2019 ◽  
Author(s):  
Daniel Fullmer ◽  
Ji Liu ◽  
A. Stephen Morse
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distributed Algorithm ◽  
Necessary Conditions ◽  
Sufficient Conditions

scholarly journals Fixed Point Theorems for Generalized αs-ψ-Contractions with Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Zhenhua Ma ◽  
Muhammad Nazam ◽  
Sami Ullah Khan ◽  
Xiangling Li
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Elliptic Boundary ◽  
Sufficient Conditions ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Unique Common Fixed Point

We study the sufficient conditions for the existence of a unique common fixed point of generalized αs-ψ-Geraghty contractions in an αs-complete partial b-metric space. We give an example in support of our findings. Our work generalizes many existing results in the literature. As an application of our findings we demonstrate the existence of the solution of the system of elliptic boundary value problems.

scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

scholarly journals A Distributed Approach to the Evasion Problem

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 149
Author(s):  
Denis Khryashchev ◽  
Jie Chu ◽  
Mikael Vejdemo-Johansson ◽  
Ping Ji
Keyword(s):  
Distributed Algorithm ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Movement Pattern ◽  
Sheaf Theory ◽  
Distributed Approach ◽  
Sufficient And Necessary Conditions ◽  
Evasion Problem ◽  
Over Time ◽  
Path Detection

The Evasion Problem is the question of whether—given a collection of sensors and a particular movement pattern over time—it is possible to stay undetected within the domain over the same stretch of time. It has been studied using topological techniques since 2006—with sufficient conditions for non-existence of an Evasion Path provided by de Silva and Ghrist; sufficient and necessary conditions with extended sensor capabilities provided by Adams and Carlsson; and sufficient and necessary conditions using sheaf theory by Krishnan and Ghrist. In this paper, we propose three algorithms for the Evasion Problem: one distributed algorithm extension of Adams’ approach for evasion path detection, and two different approaches to evasion path enumeration.

scholarly journals Common Fixed Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Mujahid Abbas ◽  
Bashir Ali ◽  
Yusuf I. Suleiman
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Common Solution ◽  
Contractive Mappings ◽  
Multiplicative Metric Spaces

The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature.

scholarly journals Fixed Point Of Contractive Mappings Of Integral Type Over An S^{JS}- Metric Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Kushal Roy ◽  
Mantu Saha ◽  
Ismat Beg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Integral Type ◽  
Couple Fixed Point ◽  
Contractive Mappings

We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.

scholarly journals A unified common fixed point theorem for a family of mappings

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 759-769
Author(s):  
Vijay Dalakoti ◽  
Ravindra Bisht ◽  
R.P. Pant ◽  
Mahesh Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Minimal Set ◽  
Contractive Type ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.

scholarly journals Convergence theorems of a scheme for I-asymptotically quasi-nonexpansive type mapping in Banach space

2015 ◽  
Vol 97 (111) ◽  
pp. 239-251
Author(s):  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Recent Work ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Convergence Theorems ◽  
Type Mapping ◽  
Necessary And Sufficient

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K ? K be an I-asymptotically quasi-nonexpansive type mapping and I : K ? K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type mappping in Banach spaces to a common fixed point of T and I. Also, we study the convergence of the Ishikawa iterative sequences to common fixed point for nonself I-asymptotically quasinonexpansive type mapping in Banach spaces. The results presented in this paper extend and generalize some recent work of Chang and Zhou [1], Wang [19], Yao and Wang [20] and many others.

scholarly journals Necessary and sufficient conditions for common fixed point theorems in fuzzy metric space

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
D. O’Regan ◽  
M. Abbas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fuzzy Metric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Common Fixed Point Theorems

AbstractThe aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps

Sign in / Sign up

Export Citation Format

Share Document