Common Fixed-Point Theorems For-Contractions In Bipolar-Metric Spaces And Application To Volterra Integral Equations

Abstract

In this article, we introduce the concept of bipolar -metric spaces as a generalization of bipolar metric spaces [9] and -bipolar metric spaces [17]. Two common fixed-point theorems are established for four self-mappings satisfying- contraction. The first theorem is proved by using the common limit in the range () property [16, 22] without requiring continuity of the mappings or completeness of the space, while the second theorem is proved in the framework of complete bipolar -metric spaces. Some corollaries are obtained as direct consequences of our main results. Non-trivial examples and an application to Volterra integral equations are also provided.