Open AccessExistence theorems for generalized vector equilibria with variable ordering relation
Author(s) -
Lu-Chuan Ceng,
Yeong-Cheng Liou,
ChingFeng Wen
Publication year - 2016
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.47.2016.2163
Subject(s) - mathematics , banach space , extension (predicate logic) , monotone polygon , monotonic function , fixed point theorem , relation (database) , variable (mathematics) , pure mathematics , fixed point , discrete mathematics , mathematical analysis , computer science , geometry , database , programming language
In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.