scholarly journals Fixed points and sets of multivalued contractions: an advanced survey with some new results

2021 ◽  
Vol 22 (1) ◽  
pp. 15-30
Author(s):  
Jan Andres ◽  
Jiřı́ Fišer ◽  
Lech Górniewicz
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Absolute Retracts ◽  
Continuation Principle ◽  
Nonlinear Alternative ◽  
Multivalued Contractions ◽  
Fixed Point Sets ◽  
Coupled Fixed Points

The existence of fixed points and, in particular, coupled fixed points is investigated for multivalued contractions in complete metric spaces. Multivalued coupled fractals are furthermore explored as coupled fixed points of certain induced operators in hyperspaces, i.e. as coupled compact subsets of the original spaces. The structure of fixed point sets is considered in terms of absolute retracts. We also formulate a continuation principle for multivalued contractions as a nonlinear alternative based on the topological essentiality. Two illustrative examples about coupled multivalued fractals are supplied.

scholarly journals Applications of Multivalued Contractions on Graphs to Graph-Directed Iterated Function Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
T. Dinevari ◽  
M. Frigon
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Iterated Function System ◽  
Iterated Function Systems ◽  
Complete Metric Spaces ◽  
Fixed Point Result ◽  
Iterated Function ◽  
Multivalued Contractions

We apply a fixed point result for multivalued contractions on complete metric spaces endowed with a graph to graph-directed iterated function systems. More precisely, we construct a suitable metric space endowed with a graphGand a suitableG-contraction such that its fixed points permit us to obtain more information on the attractor of a graph-directed iterated function system.

scholarly journals Fixed points of multivalued contractions via generalized class of simulation functions

2019 ◽  
Vol 38 (3) ◽  
pp. 161-176
Author(s):  
Deepesh Kumar Patel
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Complete Metric Spaces ◽  
Simulation Functions ◽  
Multivalued Contractions

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in α-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well known fixed point results of the literature. Some examples and consequence are given to  illustrate the usability of the theory.

scholarly journals Fixed Points and Stability for Integral-Type Multivalued Contractive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhefu An ◽  
Mengyao Li ◽  
Liangshi Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Integral Type ◽  
Point Sets ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
The Stability ◽  
Fixed Point Sets

The existence and iterative approximations of fixed points concerning two classes of integral-type multivalued contractive mappings in complete metric spaces are proved, and the stability of fixed point sets relative to these multivalued contractive mappings is established. The results obtained in this article generalize and improve some known results in the literature. An illustrative example is given.

scholarly journals Some fixed point theorems on equivalent metric spaces

2021 ◽  
Vol 38 (1) ◽  
pp. 139-148
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
MARIANA CUFOIAN ◽  
ADRIANA MITRE
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Complete Metric Spaces

This paper aims to analyze the existence of fixed points for mappings defined on complete metric spaces satisfying almost contractive conditions and a general contractive inequality of integral type. The existence of a fixed point is ensured by hypotheses formulated in terms of equivalent metric spaces.

scholarly journals Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Poom Kumam ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Partial Metric ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

scholarly journals Relation Theoretic (Θ,R) Contraction Results with Applications to Nonlinear Matrix Equations

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 767 ◽  
Author(s):  
Hamed Al-Sulami ◽  
Jamshaid Ahmad ◽  
Nawab Hussain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Binary Relation ◽  
Metric Spaces ◽  
Matrix Equations ◽  
Existence Of A Solution ◽  
Complete Metric Spaces ◽  
Numerical Example ◽  
Nonlinear Matrix

Using the concept of binary relation R , we initiate a notion of Θ R -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings.

scholarly journals Fixed Points Of F-Weak Contractions On Complete Metric Spaces

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
D. Wardowski ◽  
N. Van Dung
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Proper Extension

AbstractIn this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature

scholarly journals Fixed point theorems for multivalued generalized contractions of rational type in complete metric spaces

2014 ◽  
Vol 23 (1) ◽  
pp. 99-106
Author(s):  
ANCA M. OPREA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Multivalued Operators ◽  
Multivalued Contractions ◽  
Rational Type

The purpose of this paper is to present some fixed point theorems for multivalued contractions of rational type. We extend the results of I. Cabrera, J. Harjani and K. Sadarangan, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Annali dellUniversita di Ferrara, DOI 10.1007/s11565-013-0176-x, to the case of multivalued operators.

scholarly journals On contractive mappings and discontinuity at fixed points

2020 ◽  
Vol 14 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Hiranmoy Garai ◽  
Lakshmi Dey ◽  
Yeol Cho
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Open Problem ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Compact Metric Spaces ◽  
Contractive Mappings ◽  
Interesting Open Problem

This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive mappings, that is, A-contractive and A`-contractive, which are, in some sense, more appropriate than those of the important previous attempts. We establish some new fixed point results involving these two contractive mappings in compact metric spaces and also in complete metric spaces and show that these contractive mappings are not necessarily continuous at their fixed points. Finally, we suggest an applicable area, where our main results may be employed.

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