Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

Abstract

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

Fixed Point Theorems for Enriched Kannan Mappings in Cat(0) Spaces

“…In the same paper, the authors introduced and analysed the class of enriched Bianchini mappings as a super class of the class of enriched Kannan mappings. It is important to note that the class of enriched Bianchini mappings is a super class of the Bianchini mappings that was introduced in [7] and further studied in [8,20].…”