Some Novel Generalized Strong Coupled Fixed Point Findings in Cone Metric Spaces with Application to Integral Equations

Abstract

Fixed point (FP) has been the heart of several areas of mathematics and other sciences. FP is a beautiful mixture of analysis (pure and applied), topology, and geometry. To construct the link between FP and applied mathematics, this paper will present some generalized strong coupled FP theorems in cone metric spaces. Our consequences give the generalization of “cyclic coupled Kannan-type contraction” given by Choudhury and Maity. We present illustrative examples in support of our results. This new concept will play an important role in the theory of fixed point results and can be generalized for different contractive-type mappings in the context of metric spaces. In addition, we also establish an application in integral equations for the existence of a common solution to support our work.