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 holding () < 1 instead of () < 1 where () is the spectral radius of and ≥ 1 is the coefficient of the underlying cone-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 () < 1 by introducing some proper examples.