Two Perov type generalized graph contractions

Mujahid Abbas, Talat Nazir, Vladimir Rakočević

In $[$Približ. Metod. Rešen. Differencial'. Uravnen. extbf{2} $(1964)$, $115-134]$ A. I. Perov generalized the Banach contraction principle by employing matrices instead of contraction constants. In this paper, we introduce and study two kind of Perov type contractive mappings. Fixed point results of such mappings are obtained in the framework of cone $b$-metric spaces endowed with a graph and associated with a generalized $c$-distance. Our results and methods are new. Some corollaries and examples are presented to support the main result proved herein. These results unify, extend and generalize various comparable results in the literature. plications to quasi-singular integrals.