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

Document Type : Research Article

Author

• A. Safari-Hafshejani

Department of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 19395-3697, Tehran, Iran.

10.22067/ijnao.2023.79068.1188

Abstract

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 a modulus of convexity of power type. As a result, we obtain priori and posteriori error estimates of Zlatanov for approximating the best proximity points of
cyclic contraction maps on this type of space.

Keywords

• Fixed point
• Noncyclic contraction map
• Uniformly convex Ba-nach space
• Modulus of convexity
• Priori and posteriori errors estimates

20.1001.1.24236977.2023.13.3.2.7

Main Subjects

• Numerical Analysis

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