Abstract

The objective of this paper is to present a comparative study of mapping in Metric Space and Controlled Metric Space. The study provides the structure, gap analysis and application of Metric Space and Controlled Metric Space. A Comparative Study of Mappings in Metric Space and in Controlled Metric Space is done with the help of studying the concept of metric space, its various types of mappings. Following this, a further conceptualization of Controlled Metric Space with its various types of mappings and its applications is done. A Controlled Metric Space is a specialized concept in Mathematics that is used to deal with issues related to the "control" of distances and the behavior of sequences or functions within a metric space. And finally we compare various mappings in metric space with various mappings in controlled metric spaces. In this way we find comparative results of various types of mappings. Thus the paper focuses on comparative study between metric spaces along its properties with controlled metric space and its properties.