A Note on the Mann Iteration for k-Strict Pseudocontractions in Banach Spaces

被引：1

作者：

Sipos, Andrei ^{[1
,2
]}

机构：

[1] Univ Bucharest, Fac Math & Comp Sci, Bucharest, Romania

[2] Romanian Acad, Stoilow Inst Math, Bucharest, Romania

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 01期

关键词：

Banach spaces; effective rates of asymptotic regularity; Mann iteration; proof mining; uniformly smooth Banach spaces; 47J25; 47H09; STRONG-CONVERGENCE THEOREMS; PSEUDO-CONTRACTIONS; ASYMPTOTIC REGULARITY; FIXED-POINTS; WEAK; MAPPINGS;

D O I：

10.1080/01630563.2016.1218894

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that a variant of a previously defined function can be used to characterize 2-uniform smoothness. We then obtain greatly simplified proofs of two convergence theorems in the literature using a generalization of a lemma of and the aforementioned characterization. We also more easily obtain rates of asymptotic regularity corresponding to the studied iterations. Finally, we derive a way to relate two constants which are characteristic to 2-uniformly smooth spaces.

引用

页码：80 / 90

页数：11

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