Banach fixed point theorem from the viewpoint of digital topology

Volume 9, Issue 3, pp 895--905 http://dx.doi.org/10.22436/jnsa.009.03.19

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Authors

Sang-Eon Han - Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk, 54896, Republic of Korea.

Abstract

The present paper studies the Banach contraction principle for digital metric spaces such as digital intervals, simple closed k-curves, simple closed 18-surfaces and so forth. Furthermore, we prove that a digital metric space is complete, which can strongly contribute to the study of Banach fixed point theorem for digital metric spaces. Although Ege, et al. [O. Ege, I. Karaca, J. Nonlinear Sci. Appl., 8 (2015), 237-245] studied \Banach fixed point theorem for digital images", the present paper makes many notions and assertions of the above mentioned paper refined and improved.

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Keywords

• Banach fixed point theorem
• digital contraction map
• Banach contraction principle
• digital image
• digital continuity
• digital topology.

MSC

•  47H10
•  54E35
•  68U10

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