Opial’s modulus and fixed points of semigroups of mappings

Kuczumow, Tadeusz

doi:10.1090/S0002-9939-99-04805-4

Opial’s modulus and fixed points of semigroups of mappings
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Proc. Amer. Math. Soc. 127 (1999), 2671-2678 Request permission

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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