AUTHOR=Ariza-Ruiz David , Garcia-Falset Jesus , 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/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2015.00009

DOI=10.3389/fams.2015.00009

ISSN=2297-4687

ABSTRACT=<p>In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find <italic>p</italic> ∈ <italic>X</italic> such that <italic>Tp</italic> = <italic>Sp</italic>, where <italic>X</italic> is a nonempty set, <italic>Y</italic> is a complete metric space, and <italic>T, S</italic>:<italic>X</italic> → <italic>Y</italic> 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.</p>