Periodic Points for Various Mappings in Generalized Gauge Type Metric Spaces

Abstract

The clarity and effectiveness of fixed point theory has motivated several researchers to explore it not only in single valued but also in multi-valued mappings. Banach contraction principle has attained its fame in case of single valued mapping and attracted various authors for many years. The principle assures the uniqueness and existence of fixed point of specific self-maps on complete metric spaces and gives a powerful tool to estimate the fixed point. The panoptic and comprehensive aspect of Banach fixed point theorem has led to a number of generalizations of the result. Banach contraction principle is expanded by Nadler to multi valued mappings using the idea of Hausdorff metric spaces. The frequent appearance of fixed point theory in modern scientific fields has forced researchers to analyze this field from more general point of view. From various aspects this field has been explored such as by generalization of metric spaces and the contraction conditions.