Error estimates for approximating fixed points and best proximity points for noncyclic and cyclic contraction mappings

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 اسفند 1401

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.79068.1188

نویسنده

Akram Safari-Hafshejani^*

Department of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 193953697, Tehran, Iran.

چکیده

In this article, we find a priori and a posteriori error estimates of the fixed point for the Picard iteration associated with a noncyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type. As a result, we obtain prior and posterior error estimates of Zlatanov for approximation of the best proximity points of cyclic contraction maps on this type of space.

کلیدواژه‌ها

Fixed point؛ Noncyclic contraction map؛ Uniformly convex Banach space؛ Modulus of convexity؛ error estimate