Genericity and porosity in fixed point theory: a survey of recent results

Fixexd point theory and applications

Simeon Reich¹  Alexander J Zaslavski¹ 

[1] Department of Mathematics, The Technion - Israel Institute of Technology, Haifa, Israel

关键词: approximate fixed point;    Baire category;    Banach space;    bounded linear regularity;    complete metric space;    contractive mapping;    fixed point;    holomorphic mapping;    hyperbolic space;    infinite product;    nonexpansive mapping;    porous set;    set-valued mapping;    weak ergodic theorem;    37C20;    46G20;    46T25;    47H09;    47H10;    54E50;    54E52;    54H25;   

DOI  :  10.1186/s13663-015-0444-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We survey recent results regarding genericity and porosity in fixed point theory. These results concern, inter alia, infinite products, nonexpansive mappings, approximate fixed points, contractive mappings, bounded linear regularity, set-valued mappings, holomorphic mappings and weak ergodic theorems. We consider both normed linear spaces and hyperbolic metric spaces.

【 授权许可】

CC BY