Open AccessExistence, 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
Author(s) -
Binayak S. Choudhury,
Nikhilesh Metiya,
Sunirmal Kundu,
Priyam Chakraborty
Publication year - 2022
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/namc.2022.27.25191
Subject(s) - uniqueness , mathematics , fixed point , fixed point theorem , property (philosophy) , metric space , stability (learning theory) , fixed point property , mathematical analysis , fixed point iteration , metric (unit) , complete metric space , pure mathematics , computer science , philosophy , epistemology , machine learning , operations management , economics
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.