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 - Choudhury, Binayak S.; Metiya, Nikhilesh; Kundu, Sunirmal; Chakraborty, Priyam (Nonlinear Analysis: Modelling and Control, 2022)
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.
Keywords: fixed point; Ulam–Hyers stability; well-posedness; data dependence; Fredholm-type nonlinear integral equation