A new vector quasi-equilibrium-like problem
Commun. Korean Math. Soc. 2009 Vol. 24, No. 4, 523-528
https://doi.org/10.4134/CKMS.2009.24.4.523
Printed December 1, 2009
Byung-Soo Lee
Kyungsung University
Abstract : In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a $c$-diagonal qua-si-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the $c$-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].
Keywords : vector quasi-equilibrium-like problem, $c$-diagonally quasi-convex, open lower sections, Browder fixed point theorem
MSC numbers : 49J40
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