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Opial's modulus and fixed points
of semigroups of mappings


Author: Tadeusz Kuczumow
Journal: Proc. Amer. Math. Soc. 127 (1999), 2671-2678
MSC (1991): Primary 47H10, 46B20
DOI: https://doi.org/10.1090/S0002-9939-99-04805-4
Published electronically: March 16, 1999
MathSciNet review: 1486740
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Abstract: If $X$ is a Banach space with the non-strict Opial property and $r_{X}\left ( 1\right ) >0$ and $C$ is a nonempty convex weakly compact subset of $X$, then every semigroup $\mathfrak{T}=\left \{ T_{t}:t\in G\right \} $ of asymptotically regular selfmappings of $C$ with $\sigma \left ( \mathfrak{T}\right ) <1+r_{X}\left ( 1\right ) $ has a common fixed point.


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Additional Information

Tadeusz Kuczumow
Affiliation: Instytut Matematyki, UMCS, 20-031 Lublin, Poland
Email: tadek@golem.umcs.lublin.pl

DOI: https://doi.org/10.1090/S0002-9939-99-04805-4
Keywords: Opial's modulus, semigroups of mappings, fixed points
Received by editor(s): February 27, 1997
Received by editor(s) in revised form: September 25, 1997, and November 14, 1997
Published electronically: March 16, 1999
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society

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