A Study of Fixed Point Theorems in Fuzzy Metric Spaces and Fuzzy Graphs

Abstract

From Freschets characterization of metric room in early twentieth century, the different generalizations of metric spaces like Menger spaces, fuzzy metric spaces, intuitionistic fuzzy metric spaces, L fuzzy metric areas and others, were obtained. The idea of a fuzzy metric area as a result of J.Michalek and O.Kramosil, P.Veeramani and A.George has numerous benefits in evaluation because numerous results and notions from classical metric room principle could be lengthy as well as generalized to the setting of fuzzy metric spaces, for instance: the notion of completeness, conclusion of areas in additionto extension of maps. newlineIt proved a turningpoint in the improvement of mathematics if the idea of fuzzy set was launched by Zadeh that laid the foundation of fuzzy mathematics. Consequently the final 3 years had been extremely effective for fuzzy mathematics and the latest literature has noticed the fuzzification in nearly every path of mathematics including arithmetic, probability theory, graph theory, topology, reason etc. Fuzzy set principle has uses in applied sciences such as for instance neural community concept, balance concept, mathematical programming, modeling concept, engineering sciences, health newlinesciences (medical genetics, nervous system), control theory, image processing, correspondence etc. Not surprising that fuzzy fixed point principle is now a location of attention for experts in fixed point concept, or maybe fuzzy mathematics has provided brand new choices for fixed point theorists. newlineThe principle of fixed areas is in the hands of topology, a department of mathematics produced in the conclusion of the nineteenth century, and also makes extensive use of such topological notions as continuity, newlinehomotophy, compactness, as well as the level of mapping. The metric areas are fundamental in the research of functional analysis and topology. Not too long ago the metric areas have received benefits because of the improvement of the metric fixed stage principle.