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

Laszlo Balog, Vasile Berinde

Let K be a non-empty closed subset of a Banach space X endowed with a graph G. The main result of this paper is a fixed point theorem for nonself Kannan GG-contractions T:KXT:K→X that satisfy Rothe’s boundary condition, i.e., TT maps K∂K (the boundary of KK) into KK. 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.

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Berinde, Vasile, Balog Laszlo