Uniform asymptotic normal structure, the uniform semi-opial property, and fixed points of asymptotically regular uniformly Lipschitzian semigroups. II.

Budzyńska, Monika; Kuczumow, Tadeusz; Reich, Simeon

Displaying similar documents to “Uniform asymptotic normal structure, the uniform semi-opial property, and fixed points of asymptotically regular uniformly Lipschitzian semigroups. II.”

Uniform asymptotic normal structure, the uniform semi-Opial property and fixed points of asymptotically regular uniformly Lipschitzian semigroups. I.

Budzyńska, Monika, Kuczumow, Tadeusz, Reich, Simeon (1998)

Abstract and Applied Analysis

Similarity:

Fixed points of Lipschitzian semigroups in Banach spaces

Jarosław Górnicki (1997)

Studia Mathematica

Similarity:

We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = T_{s} : C \to C : s \in G = [0, \infty)$ is a Lipschitzian semigroup such that $g = l i m i n f_{G ∋ α \to \infty} i n f_{G ∋ δ \geq 0} 1 / α ʃ_{0}^{α} ∥ T_{β + δ} ∥^{p} d β < 1 + c$ , where c > 0 is some constant, then there exists x ∈ C such that $T_{s} x = x$ for all s ∈ G.