A generalization of Hardy-Rogers theorem in generalized b-metric spaces

Abstract

In this paper, some common fixed point results for singlevalued and multivalued operators satisfying generalized contractive condition in a generalized b-metric spaces are proved. Advantage of our work in comparison with studies done in the context of b-metric is that, the b-metric functions used in the theorems are not necessarily continuous. So, our results extend and improve several comparable results obtained previously. To show the validity of our work, we also prove that the same results hold even if the space is endowed with two metrics.