Vol. 18(2017) No. 2

 

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  Vector equilibrium problems for multifunctions in topological semilattice spaces
 
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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 , where is the set of all fixed points of the multifunction A: K → 2K 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, CΔ-quasiconvex (quasiconcave), C-upper (lower) semicontinuous, vector equilibrium problem.

2010 Mathematics Subject Classification: 47H10, 47J20, 49J40.

Published on-line: June 1st, 2017.

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