scholarly journals Fixed Point, Data Dependence, and Well-Posed Problems for Multivalued Nonlinear Contractions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Iram Iqbal ◽  
Nawab Hussain ◽  
Hamed H. Al-Sulami ◽  
Shanza Hassan
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Data Dependence ◽  
Well Posedness ◽  
Nonlinear Operators ◽  
Complete Metric Spaces ◽  
Multivalued Operators ◽  
Point Data ◽  
Well Posed ◽  
Nonlinear Contractions

The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature.

scholarly journals Well-posedness of fixed point problem for mappings satisfying an implicit relation

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Mohamed Akkouchi ◽  
Valeriu Popa
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Implicit Relation ◽  
Complete Metric Spaces ◽  
Well Posed

AbstractThe notion of well-posedness of a fixed point problem has generated much interest to a several mathematicians, for example, F. S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B. K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). The aim of this paper is to prove for mappings satisfying some implicit relations in orbitally complete metric spaces, that fixed point problem is well-posed.

scholarly journals Existence, uniqueness, Ulam–Hyers–Rassias stability, well-posedness and data dependence property related to a fixed point problem in gamma-complete metric spaces with application to integral equations

2022 ◽  
Vol 27 (1) ◽  
pp. 121-141
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Sunirmal Kundu ◽  
Priyam Chakraborty
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Point Problem ◽  
Well Posedness ◽  
Complete Metric Spaces ◽  
Continuity Assumption ◽  
Dependence Property ◽  
Rassias Stability

In this paper, we study a fixed point problem for certain rational contractions on γ-complete metric spaces. Uniqueness of the fixed point is obtained under additional conditions. The Ulam–Hyers–Rassias stability of the problem is investigated. Well-posedness of the problem and the data dependence property are also explored. There are several corollaries of the main result. Finally, our fixed point theorem is applied to solve a problem of integral equation. There is no continuity assumption on the mapping.

RANDOM COINCIDENCE AND FIXED POINTS FOR WEAKLY COMPATIBLE MAPPINGS IN CONVEX METRIC SPACES

2009 ◽  
Vol 02 (02) ◽  
pp. 171-182 ◽  
Author(s):  
Izmat Beg ◽  
Adnan Jahangir ◽  
Akbar Azam
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Coincidence Points ◽  
Random Coincidence ◽  
Complete Metric Spaces ◽  
Random Fixed Points ◽  
Weakly Compatible ◽  
Convex Metric Spaces

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.

Hybrid fixed points of multivalued operators in metric spaces with applications

2009 ◽  
Vol 70 (11) ◽  
pp. 4106-4117 ◽  
Author(s):  
Shihuang Hong ◽  
Dongxue Guan ◽  
Li Wang
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Multivalued Operators

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.

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