Common Fixed Point Results in G b Metric Space and Generalized Fuzzy Metric Space Using E.A Property and Altering Distance Function

Abstract

Fuzzy logic is a new scientific field which is employed in mathematics, computer science and engineering. Fuzzy logic calculates the extent to which a proposition is correct and allows computer to manipulate the information. In this paper, our objective is to prove fixed point results in the setting of G b metric space and generalized fuzzy metric space. The concept of G b metric space is given by Aghajani in 2013, which is generalization of G-metric space and b metric space. Sedghi et al., proved results on G b metric space using continuity and commutativity. Also, the notion of generalized Fuzzy metric space is given by Sung and Yang. In 2011, Rao et al., proved results in generalized fuzzy metric space using w-compatible mappings. Here, to prove the results notion of E.A property, weakly compatible property and contractive type condition have been utilized. Our results extend and generalize the results of many authors existing in the literature. An example has also been given to justify the result.