Nadler mappings in cone b-metric spaces over Banach algebras

Abstract

In this study we first define the concept of Nadler type contraction in the setting of H-cone b-metric space with respect to cone b-metric spaces over Banach algebras. Next we prove the Banach contraction principle for such contractions by means of the notion of spectral radius and a solid cone in underlying Banach algebra. Finally we observe that the main result achieved in this work extends and generalizes the well known results associated with contractions of Nadler type.