Weak uniform normal structure and fixed points of asymptotically regular semigroups
Let \(X\) be a Banach space with a weak uniform normal structure and let \(C\) be some (nonempty) convex weakly compact subset of it. Then each asymptotically regular semigroup \(T=(T(t);t\in S)\) of weakly continuous selfmaps on \(C\) with \(\liminf_{S\ni t\to \infty} L(T(t))< WCS(X)\) has a common fixed point. Here, \(L(T(t))\) is the exact Lipschitz constant of \(T(t)\) and \(WCS(X)\) is the weakly convergent sequence coefficient of \(X\).
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