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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fixed point theorems in reflexive Banach spaces


Author: R. Kannan
Journal: Proc. Amer. Math. Soc. 38 (1973), 111-118
MSC: Primary 47H10
MathSciNet review: 0313896
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Abstract: In this paper fixed point theorems are established first for mappings $ T$, mapping a closed bounded convex subset $ K$ of a reflexive Banach space into itself and satisfying

$\displaystyle \vert\vert Tx - Ty\vert\vert \leqq \tfrac{1}{2}\{ \vert\vert x - Tx\vert\vert + \vert\vert y - Ty\vert\vert,\quad x,y \in K,$

and then an analogous result is obtained for nonexpansive mappings giving rise to a question regarding the unification of these theorems.

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DOI: https://doi.org/10.1090/S0002-9939-1973-0313896-2
Article copyright: © Copyright 1973 American Mathematical Society