Fixed point theorems in reflexive Banach spaces
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- by R. Kannan PDF
- Proc. Amer. Math. Soc. 38 (1973), 111-118 Request permission
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 \[ ||Tx - Ty|| \leqq \tfrac {1}{2}\{ ||x - Tx|| + ||y - Ty||,\quad x,y \in K,\] and then an analogous result is obtained for nonexpansive mappings giving rise to a question regarding the unification of these theorems.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 111-118
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313896-2
- MathSciNet review: 0313896