Banach fixed point theorem from the viewpoint of digital topology
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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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ISRP Style
Sang-Eon Han, Banach fixed point theorem from the viewpoint of digital topology, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 895--905
AMA Style
Han Sang-Eon, Banach fixed point theorem from the viewpoint of digital topology. J. Nonlinear Sci. Appl. (2016); 9(3):895--905
Chicago/Turabian Style
Han, Sang-Eon. "Banach fixed point theorem from the viewpoint of digital topology." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 895--905
Keywords
- Banach fixed point theorem
- digital contraction map
- Banach contraction principle
- digital image
- digital continuity
- digital topology.
MSC
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