A combinatorial lemma and its applications
AbstractIn 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.
|Journal series||Journal of Inequalities and Applications, ISSN 1029-242X, [1025-5834], (A 30 pkt)|
|Publication size in sheets||1.05|
|Keywords in English||Browder fixed point theorem, combinatorial methods, continuum of zeros, equilibrium, fixed point, Kakutani fixed point theorem, Sperner lemma, zero of a map|
|ASJC Classification||; ;|
|Score|| = 20.0, 16-12-2019, ArticleFromJournal|
= 30.0, 16-12-2019, ArticleFromJournal
|Publication indicators||= 0; : 2016 = 0.733; : 2016 = 0.791 (2) - 2016=0.82 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.