Recent results on the topological fixed point theory of multivalued mappings: a survey

Fixexd point theory and applications

Lech Gó¹  Jan Andres²  rniewicz³ 

[1] University, Olomouc, Czech Republic;Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, PalackýInstitute of Mathematics, University of Kazimierz Wielki, Bydgoszcz, Poland

关键词: fixed points;    multivalued mappings;    fixed point index;    Lefschetz fixed point theorem;    ejective and repulsive fixed points;    absolute neighborhood retracts and multiretracts;    random operators;    random fixed points;    differential inclusions;    multivalued fractals;    55M20;    54C60;    55M15;    54H25;    47H04;    47H10;    47H40;    34F05;    28A80;    34A60;   

DOI  :  10.1186/s13663-015-0432-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this survey, we present current results from the topological fixed point theory of multivalued mappings which were obtained by ourselves in the last five years (see Andres and Górniewicz in Fixed Point Theory 12(2):255-264, 2011; Topol. Methods Nonlinear Anal. 40:337-358, 2012; Libertas Mathematica 33(1):69-78, 2013; Int. J. Bifurc. Chaos 24(11):1450148, 2014; J. Nonlinear Convex Anal. 16(6):1013-1023, 2015; Int. J. Bifurc. Chaos, 2015, to appear). Some abstract theorems are applied to differential inclusions and multivalued fractals. A part of the deterministic theory is randomized, including the applications to random differential inclusions.

【 授权许可】

CC BY