A new fixed-point theorem for contractive mappings.
In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.
Let be a closed convex subset of a complete convex metric space . In this paper a class of selfmappings on , which satisfy the nonexpansive type condition below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
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