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

Let be a non-empty closed subset of a Banach space endowed with a graph . The main result of this paper is a fixed point theorem for nonself Kannan -contractions that satisfy Rothe’s boundary condition, i.e., maps (the boundary of ) into . Our new results are extensions of recent fixed point theorems for self mappings on metric spaces endowed with a partial order and also of various fixed point theorems for self and nonself mappings on Banach spaces or convex metric spaces.