Fixed Point in Finite Neutrosophic Topological Metric Space

Abstract

Briefly, neutrosophy is a new branch of philosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. It relates to a general form of logic in which each proposition has separate values for truth, falsehood, and indeterminacy. This was formally discovered by Florentin Smarandache. For instance, the Neutrosophic sets (NS) have a significant role for clustering, denoising, segmentation, and classification in numerous medical image-processings as well as their general applications. Motivated by the above, in this paper, we show that if Y (I) is a complete neutrosophic metric space in which the function f is a contracting mapping on the neutrosophic metric space Y (I), then, there exists one and only one point v in Y (I) such that f (v) = v