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Minimax Theory and its Applications 03 (2018), No. 1, 057--072
Copyright Heldermann Verlag 2018

Quasi-Equilibrium Problems and Fixed Point Theorems of the Sum of l.s.c. and u.s.c. Mappings

Nguyen Xuan Tan
Institute of Mathematics, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam

Nguyen Quynh Hoa
Thai Nguyen University of Economics and Business Administration, Tan Thinh Ward, Thai Nguyen City, Vietnam

Nguyen Ba Minh
University of Commerce, Hanoi, Vietnam

We first formulate generalized quasi-equilibrium problems concerning multivalued mappings and give some sufficient conditions to the existence of their solutions. In particular, we establish several results on the existence of fixed points of the sum of l.s.c. and u.s.c. mappings. These generalize some well-known fixed point theorems obtained by previous authors as Ky Fan, F. E. Browder and Ky Fan, X. Wu, L. J. Lin, and Z. T. Yu, etc. Lastly, we apply the obtained results to quasi-equilibrium problems of types I, II and mixed quasi-equilibrium problems of these two types.

Keywords: Generalized quasi-equilibrium problems, quasi-equilibrium problems of type I, type II, mixed equasi-equilibrium problems, upper semi-continuous mapping, lower semi-continuous mapping, fixed point theorem.

MSC: 49J27, 49J53, 91B50, 90C48

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