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.

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 Fixed Point Problems on Generalized Metric Spaces in Perov’s Sense

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 856
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota ◽  
Asim Naseem
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Fixed Point Problems ◽  
Symmetry Condition ◽  
Point Problem ◽  
Well Posedness ◽  
Generalized Metric Spaces ◽  
Generalized Metric

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov’s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy–Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam–Hyers stability of the fixed point problem. An example is also given to sustain the presented results.

scholarly journals On Some New Multivalued Results in the Metric Spaces of Perov’s Type

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 438
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota ◽  
Asim Naseem ◽  
Zoran D. Mitrović ◽  
Manuel de la Sen ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Point Problem ◽  
Contractive Condition ◽  
Well Posedness ◽  
Fixed Point Set ◽  
Generalized Metric Spaces ◽  
Point Set

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov’s sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam–Hyers stability are also studied.

scholarly journals Fixed point results for multivalued hardy-rogers contractions in b-metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2499-2507 ◽  
Author(s):  
Cristian Chifu ◽  
Gabriela Petruşel
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Data Dependence ◽  
Point Problem ◽  
Contractive Condition ◽  
Well Posedness ◽  
Fixed Point Set ◽  
Point Set

The purpose of this paper is to present some fixed point results in b-metric spaces using a contractive condition of Hardy-Rogers type with respect to the functional H. The data dependence of the fixed point set, the well-posedness of the fixed point problem, as well as, the Ulam-Hyres stability are also studied.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

scholarly journals Some Fixed-Point Results via Mix-Type Contractive Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Özlem Acar
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Rational Type ◽  
Type Contraction

We consider a fixed-point problem for mappings involving a rational type and almost type contraction on complete metric spaces. To do this, we are using F -contraction and H , φ -contraction. We also present an example to illustrate our result.

scholarly journals Generalized Ulam-Hyers Stability, Well-Posedness, and Limit Shadowing of Fixed Point Problems forα-β-Contraction Mapping in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Banach Contraction ◽  
Limit Shadowing ◽  
New Type ◽  
The Banach Contraction Principle

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-calledα-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3365-3379 ◽  
Author(s):  
Z. Ahmadi ◽  
R. Lashkaripour ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Complete Metric Spaces ◽  
New Class ◽  
Constraint Inequalities ◽  
Weaker Conditions

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our results.

scholarly journals Multivalued fixed point theorem in b-metric spaces and its application to differential inclusions

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2963-2976
Author(s):  
Maher Berzig ◽  
Imed Kédim ◽  
Aymen Mannai
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Multivalued Mappings ◽  
Point Problem ◽  
Contractive Condition ◽  
Well Posedness ◽  
Shadowing Property ◽  
Limit Shadowing

Our purpose in this paper is to present a fixed point result for multivalued mappings satisfying nonlinear quasi-contractive condition only on related points. Moreover, we provide a qualitative study of well-posedness, limit shadowing property and Ulam-Hyers stability of our fixed point problem. As application, we discuss the existence of a unique solution for a class of differential inclusions.

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