Some aspects of a coupled system of nonlinear integral equations - CHOUDHURY, Binayak S.; METIYA, Nikhilesh; KUNDU, Sunirmal (Studia Universitatis Babeș-Bolyai Mathematica, 2024)
In the present paper, we take a system of two integral equations and prove the existence and uniqueness of their solution. We investigate four aspects of the problem, namely, error estimation and rate of convergence of the iteration leading to the solution, Ulam-Hyers stability, well-posedness and data dependence of the solution sets. We give some new definitions pertaining to the system we analyze here. In order to establish our results, we utilize the coupled contraction mapping principle due to Bhaskar and Lakshmikantham (Nonlinear Anal. TMA 65(2006), 1379-1393) and several related results which we deduce here. Mathematics Subject Classification (2010): 54H10, 54H25, 47H10.