Quasi-Contractions In Banach Spaces
Let be a closed convex subset of a complete convex metric space and two compatible mappings satisfying following contraction definition: for all in , where and . If is continuous and contains , then and have a unique common fixed point in and at this point is continuous. This result gives affirmative answers to open questions set forth by Diviccaro, Fisher and Sessa in connection with necessarity of hypotheses of linearity and non-expansivity of in their Theorem [3]...
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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