A Proper Generalization of Banach Principle for Nadler Type Mappings in Cone b-Metric Spaces Over Banach Algebras

Abstract

In this paper, we first consider Nadler type contractions with the generalized Lipschitz constant k holding r(k)<1 instead of r(sk)<1 where r(k) is the spectral radius of k and s≥1 is the coefficient of the underlying cone b-metric spaces over Banach algebras. Then, we prove the corresponding fixed point theorem for such mappings. Finally, we compare our result with one obtained by the case r(sk)<1 by introducing some proper examples.