@ARTICLE{10.3389/fams.2015.00009, AUTHOR={Ariza-Ruiz, David and Garcia-Falset, Jesus and Sadarangani, Kishin}, TITLE={Wardowski conditions to the coincidence problem}, JOURNAL={Frontiers in Applied Mathematics and Statistics}, VOLUME={1}, YEAR={2015}, URL={https://www.frontiersin.org/articles/10.3389/fams.2015.00009}, DOI={10.3389/fams.2015.00009}, ISSN={2297-4687}, ABSTRACT={In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ 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 toward the solution of a second order differential equation.} }