scholarly journals WELL POSEDNESS OF FIXED POINT PROBLEM FOR MAPPINGS SATISFYING AN IMPLICIT RELATION IN Gp - METRIC SPACES

2015 ◽  
Vol 3 (1) ◽  
pp. 108-117
Author(s):  
Valeriu POPA ◽  
Alina-mihaela PATRICIU
2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Mohamed Akkouchi ◽  
Valeriu Popa

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.


2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wutiphol Sintunavarat

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.


2022 ◽  
Vol 27 (1) ◽  
pp. 121-141
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Sunirmal Kundu ◽  
Priyam Chakraborty

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.


Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2963-2976
Author(s):  
Maher Berzig ◽  
Imed Kédim ◽  
Aymen Mannai

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.


Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 856
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota ◽  
Asim Naseem

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.


Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 438
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota ◽  
Asim Naseem ◽  
Zoran D. Mitrović ◽  
Manuel de la Sen ◽  
...  

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.


2022 ◽  
Vol 7 (4) ◽  
pp. 5199-5219
Author(s):  
Anam Arif ◽  
◽  
Muhammad Nazam ◽  
Aftab Hussain ◽  
Mujahid Abbas ◽  
...  

<abstract><p>In this paper, we introduce an ordered implicit relation. We present some examples for the illustration of the ordered implicit relation. We investigate conditions for the existence of the fixed points of an implicit contraction. We obtain some fixed point theorems in the cone $ b $-metric spaces and hence answer a fixed-point problem. We present several examples and consequences to explain the obtained theorems. We solve an homotopy problem and show existence of solution to a Urysohn Integral Equation as applications of the obtained fixed point theorem.</p></abstract>


Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2499-2507 ◽  
Author(s):  
Cristian Chifu ◽  
Gabriela Petruşel

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.


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