Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2017; 32(4): 933-957

Online first article August 25, 2017      Printed October 31, 2017

https://doi.org/10.4134/CKMS.c170002

Copyright © The Korean Mathematical Society.

Generalized bi-quasi-variational-like inequalities on non-compact sets

Yeol Je Cho, Mohammad S. R. Chowdhury, Je Ai Ha

Gyeongsang National University, University of Management and Technology (UMT), Gyeongsang National University

Abstract

In this paper, we prove some existence results of solutions for a new class of generalized bi-quasi-variational-like inequalities (GBQVLI) for ($\eta$-$h$)-quasi-pseudo-monotone type I and strongly ($\eta$-$h$)-quasi-pseudo-monotone type I operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. To obtain our results on GBQVLI for ($\eta$-$h$)-quasi-pseudo-monotone type I and strongly ($\eta$-$h$)-quasi-pseudo-monotone type I operators, we use Chowdhury and Tan's generalized version of Ky Fan's minimax inequality as the main tool.

Keywords: generalized bi-quasi-variational-like inequalities, ($\eta$-$h$)-quasi-pseudomonotone type I operators, locally convex Hausdorff topological vector spaces

MSC numbers: 49J30, 47H10, 47H17, 49M05

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