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A fixed point theorem involving a hybrid inwardness-contraction condition

✍ Scribed by Hoang Tuy

Publisher: John Wiley and Sons
Year: 1981
Tongue: English
Weight: 245 KB
Volume: 102
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19811020122

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✦ Synopsis

Abstract

A fixed point theorem is proved which involves a hybrid inwardness‐contraction condition and simultaneously extends three earlier results of NADLER, CLARKE and REICH, respectively.

The aim of this paper is to prove a fixed point theorem which will simultaneously extends three earlier results of NADLER [5], CLARKE [2], and REICH [7], respectively.

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Let D be a closed nonempty subset of a Banach space X and T : D ª X Ä 4 2 \_ a multivalued contraction with closed values, i.e., each Tx is a nonempty closed subset of X and there exists 0 F k -1 such that 5 5 H Tx, Ty F k x y y , x, y g D, ## Ž . where H denotes the Hausdorff metric H A, B s ma