Uniform asymptotic normal structure, the uniform semi‐Opialproperty, and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part II

Monika Budzyńska,Tadeusz Kuczumow,Simeon Reich

doi:10.1155/s1085337598000554

Monika Budzyńska, Tadeusz Kuczumow + Show 1 more

Open Access

https://doi.org/10.1155/s1085337598000554

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Abstract

In this part of our paper we present several new theorems concerning the existence of common fixed points of asymptotically regular uniformly lipschitzian semigroups.

Highlights

Let (X, · ) be a Banach space and C a subset of X
Every asymptotically regular sequence {xn} with a weakly compact conv {xn} there exists a weakly convergent to w subsequence {xni} such that (i) r (w, {xni}) ≤ θ · diama ({xn}), (ii) w − y ≤ ra (y, {xni}) for every y ∈ X
We find i0 such that for all i ≥ i0 we have

Summary

Introduction

Let (X, · ) be a Banach space and C a subset of X. [30] Let X be a uniformly convex Banach space, C a nonempty bounded closed convex subset of X and T : C → C a k-lipschitzian mapping with k < γ1, where γ1 > 1 is the solution of the equation γ1 1 − δ [7] Let X be a Banach space X with uniform normal structure and C a nonempty bounded closed convex subset of X.

Results

Conclusion