A combinatorial lemma and its applications

Journal of inequalities and applications

Piotr Mać¹ 

关键词: Browder fixed point theorem;    combinatorial methods;    continuum of zeros;    equilibrium;    fixed point;    Kakutani fixed point theorem;    Sperner lemma;    zero of a map;    91B02;    91B50;    54H25;   

DOI  :  10.1186/s13660-016-1043-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we present a generalization of a combinatorial lemma we stated and proved in a recent work. Then we apply the generalized lemma to prove: (1) a theorem on the existence of a zero for an excess demand mapping, (2) the existence of a continuum of zeros for a parameterized excess demand mapping, (3) Sperner’s lemma on labelings of triangulations. Proofs of these results are constructive: they contain algorithms (based on the combinatorial lemma) for the computation of objects of interest or, at least, of their approximations.

【 授权许可】

CC BY