Strict contractive conditions and common fixed point theorems with application

Abstract

Abstract The aim of the present paper is to obtain common fixed point theorems under a strict contractive condition by assuming minimal commutativity conditions. Our theorems extend the results due to Pant and Pant [4]. In the setting of our results, we also provide pair of mappings which ensures the existence of a common fixed point; however, both the mappings are discontinuous at the common fixed point. We, thus, provide one more answer to the problem of Rhoades [10]. In the last section, we apply our results to solve an eigenvalue problem.