Banach fixed point theorem from the viewpoint of digital topology

The present paper studies the Banach contraction principle for digital metric spaces such as digital intervals, simple closed kcurves, simple closed 18surfaces 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.