Banach and Edelstein Fixed Point Theorems for Digital Images

Akram Hossain^1, , Razina Ferdausi², Samiran Mondal¹ and Harun Rashid¹

¹Department of Mathematics, Jessore University of Science & Technology, Jessore, Bangladesh

²Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

Cite this paper:
Akram Hossain, Razina Ferdausi, Samiran Mondal and Harun Rashid. Banach and Edelstein Fixed Point Theorems for Digital Images. Journal of Mathematical Sciences and Applications. 2017; 5(2):36-39. doi: 10.12691/jmsa-5-2-2

Abstract

The current paper generalizes the Edelstein fixed point theorem for digital (ε,k)-chainable metric spaces. In order to generalize Edelstein fixed point theorem, we study the digital topological properties of digital images. Further, we establish the Banach fixed point theorem for digital images. We give the notion of digital (ε,λ,k)-uniformly locally contraction mapping on digital (ε,k) -chainable metric spaces Finally, we generalize the Banach fixed point theorem to digital (ε,k)-chainable metric spaces which is known as the Edelstein fixed point theorem for digital images on digital (ε,k)-chainable metric spaces.

Keywords:
digital image digital continuity digital metric space digital (ελk)-uniformly locally contraction digital (εk)-chainable metric space Banach fixed point theorem Edelstein fixed point theorem

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