A new existence theorem of maximal elements in non-compact \(H\)-spaces with applications to minimax inequalities and variational inequalities
The authors investigate maximal elements problems in noncompact \(H\)-spaces. They introduce the notion of \(W\)-correspondence generalizing the \(L\)-correspondence and derive new existence theorems of maximal elements. Their results improve and extend the corresponding results of \textit{N. C. Yannelis} and \textit{N. D. Prabhakar} [J. Math. Econ. 12, 223-245 (1983; Zbl 0536.90019)], \textit{K.-K. Tan, J. Yu} and \textit{X.-Z. Yuan} [Nonlinear Anal., Theory Methods Appl. 24, No. 10, 1457-1470 (1995; Zbl 0836.90150)], \textit{J. X. Zhou} and \textit{G. Chen} [J. Math. Anal. Appl. 132, No. 1, 213-225 (1988; Zbl 0649.49008)], and \textit{C.-L. Yen} [Pac. J. Math. 97, 477-481 (1981; Zbl 0493.49009)]. As applications two extended versions of the Fan-Yen minimax inequality are obtained and the existence of solutions of variational and quasi-variational inequalities are studied.
variational and quasi-variational inequality
scientific article; zbMATH DE number 1288329