On new extended cone b-metric-like spaces over a real Banach algebra

Abstract

Abstract In this article, we introduce the structure of a new extended cone b-metric-like space over a Banach algebra. In this generalized space, we define the notion of generalized Reich-type mappings and prove a fixed point result. We also prove a fixed point result using α ∗ − ψ $\alpha^{\ast}-\psi$ multivalued contraction and provide some of its consequences. Finally, we furnish with applications to establish the validity of our results.

Keywords

• Cone metric space
• Reich-type mappings
• α ∗ − ψ $\alpha^{\ast}-\psi$ multivalued contraction