Wardowski conditions to the coincidence problem - Ariza-Ruiz, David; Garcia-Falset, Jesus; Sadarangani, Kishin (Frontiers in Applied Mathematics and Statistics, 2015)
In this article we □rst discuss the existence and uniqueness of a solution for the coincidence problem: Find $p \in X$ such that Tp = Sp; where X is a nonempty set, Y is a complete metric space, and $T; S : X → Y$ are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as well as a rate of convergence for this iteration scheme. Finally, we shall apply our results to study the existence and uniqueness of a solution as well as the convergence of the Picard-Juncgk iteration process towards the solution of a second order di□erential equation.