A combinatorial lemma and its applications
| Autor: | Piotr Maćkowiak |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
TheoryofComputation_MISCELLANEOUS
Browder fixed point theorem continuum of zeros 0211 other engineering and technologies Aubin–Lions lemma Kakutani fixed point theorem 02 engineering and technology Sperner's lemma equilibrium 01 natural sciences Combinatorics Discrete Mathematics and Combinatorics 0101 mathematics Euclid's lemma combinatorial methods Mathematics Discrete mathematics Lemma (mathematics) 021103 operations research lcsh:Mathematics Applied Mathematics TheoryofComputation_GENERAL Céa's lemma lcsh:QA1-939 010101 applied mathematics fixed point Teichmüller–Tukey lemma Five lemma Pumping lemma for context-free languages Analysis |
| Zdroj: | Journal of Inequalities and Applications, Vol 2016, Iss 1, Pp 1-22 (2016) |
| ISSN: | 1029-242X |
| DOI: | 10.1186/s13660-016-1043-y |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|