The Existence And Well-posedness Of Solutions To Generalized Vector Equilibrium Problems

Vector equilibrium problem is equilibrium problem of a kind of important form to promote.Equilibrium problems are widely used in the economic field,involved in mathematical economics,mechanistic,cybernetics,theory of nonlinear programming.That is the study of multi-objective and multi-layer planning important basis and tools.The generalized vector equilibrium problems is a vector equilibrium problems form of promotion.Existence of solutions and well-posedness of its is a hot topic of attention of scholars.This article mainly the existence and well-posedness of solutions to generalized vector equilibrium problems.This paper expounds the main research results as follows:Firstly mainly studies the existence of solutions of generalized vector equilibrium problems in reflexive Banach spaces.First of all,introduced the concept of vector-valued ternary mapping monotonicity,combied with Fan-KKM theorem and Nadler lemma,under certain conditions to get the existence of solutions result for generalized vector equilibrium problems in reflexive Banach space.Secondly,we also introduced the complete semicontinuity and strong semicontinuity for vector multivallued mappings.Moreover,by using the Brouwer fixed point theorem,we prove the solvability for the class of generalized vector equilibrium problems without monotonicity assumption.Secondly mainly studies the well-posedness of solutions for a class of generalized vector equilibrium problems.Thereafter we prove the well-posedness of solutions by assuming the boundedness of an approximate solution set.Moreover,we prove that well-posedness of the considered optimization problems is closely related to that of the generalized vector equilibrium problems.The obtained results generalize the some of the results of the recent literature.