Some fixed point theorems on b-metric spaces

Abstract

In this paper, we introduce new contractive mappings in the setup of completeness and uniqueness of fixed point theorem on $b$-metric space. We improve the recent fixed point results established by Agrawal et al. (Agrawal, S., Qureshi, K. and Nema, J., A fixed point theorems for $b$-metric space, IJPAM, 9(1), 2016, 45--50). We also show that different contractive type mappings exist in $b$-metric space.