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

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.

digital image, digital continuity, digital metric space, digital (ε, λ, k)-uniformly locally contraction, digital (ε, k)-chainable metric space, Banach fixed point theorem, Edelstein fixed point theorem