Wardowski conditions to the coincidence problem

Frontiers in Applied Mathematics and Statistics

Sadarangani, Kishin¹  Ariza-Ruiz, David²  Garcia-Falset, Jesus³ 

[1] Universidad de Las Palmas de Gran Canaria, Departamento de Matematicas, Las Palmas de Gran Canaria, Spain;Universidad de Sevilla, Departamento de An alisis Matem atico, Sevilla, Spain;university of Valencia, Mathematical Analysis, Dr. Moliner 50, Burjassot, 46100, Valencia, Spain

关键词: Coincidence points;    iterative methods;    Rate of convergence;    Common fixed points;    ordinary differential equations;   

DOI  :  10.3389/fams.2015.00009

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

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 $T; S : X \to Y$ 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.

【 授权许可】

CC BY