Vector equilibrium problems for multifunctions in topological semilattice spaces


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	Vector equilibrium problems for multifunctions in topological semilattice spaces


	Fixed Point Theory, Volume 18, No. 2, 2017, 741-754, June 1st, 2017 DOI: 10.24193/fpt-ro.2017.2.60 Authors: Nguyen The Vinh and Pham Thi Hoai Abstract: Let K be a nonempty compact Δ-convex subset of a topological semilattice with path-connected intervals. In this paper, under new assumptions, we establish some existence theorems of x ∈ K such that $\EuScript{F}(A)\cap VEP(f)\not=\emptyset$ , where $\EuScript{F}(A)$ is the set of all fixed points of the multifunction A: K → 2^K and VEP(f) is the set of all solutions for the vector equilibrium problems of the multifunction f from K x K to a topological vector space Y. These results generalize and improve the recent ones in the literature. Some examples are given to illustrate our results. Key Words and Phrases: KKM lemma, Ky Fan inequality, Browder-Fan fixed point theorem, multifunction, topological semilattice, C_Δ-quasiconvex (quasiconcave), C-upper (lower) semicontinuous, vector equilibrium problem. 2010 Mathematics Subject Classification: 47H10, 47J20, 49J40. Published on-line: June 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents