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

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

Category: Vol 32/2016 no. 3 Tags: Non self mapping, Kannan contraction, Fixed point, Banach space, Graph, Property (M), Rothe’s boundary condition

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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 $G$ -contractions $T: K \rightarrow X$ that satisfy Rothe’s boundary condition, i.e., $T$ maps $\partial K$ (the boundary of $K$ ) into $K$ . 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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Author(s)	Balog, Laszlo, Berinde, Vasile