Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces

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Bapurao C. Dhage


In this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under suitable conditions. Our results include the well-known result of Kannan (1968) and Bose and Mukherjee (1981) as the special cases with a different and constructive method.

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