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A new class of nonexpansive type mappings and fixed points

Ljubomir B. Ćirić — 1999

Czechoslovak Mathematical Journal

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.

On a generalization of a Greguš fixed point theorem

Ljubomir B. Ćirić — 2000

Czechoslovak Mathematical Journal

Let C be a closed convex subset of a complete convex metric space X . In this paper a class of selfmappings on C , which satisfy the nonexpansive type condition ( 2 ) below, is introduced and investigated. The main result is that such mappings have a unique fixed point.

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