Common fixed point theorem for weakly compatible mappings in Sm metric space

Abstract

In the present paper, at first, we study the structure of the newly Smmetric space, which is a union of S-metric space and multiplicative metric space with new contraction condition. We have proved a common fixed point theorem in Sm metric space by applying the concepts of the weakly compatible mappings, semi-compatible mappings, and reciprocally continuous mappings. This result generalizes and improves many common fixed point theorems in S-metric space and multiplicative metric space . Further, we also provide some examples to support our result.

Keywords

• weakly compatible mappings,reciprocally continuous mappings and semi compatible mappings.