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Keywords:
nonexpansive type mapping; asymptotically regular mapping; fixed point.
nonexpansive type mapping; asymptotically regular mapping; fixed point.
Summary:
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.
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