Some minimax type results of Clarke's generalized directional derivative and point-coderivative of multifunctions (Q1857395)

The paper is motivated by some recent results of \textit{G. Kassay} and \textit{Zs. Páles} [Nonlinear Anal. 35 A, No.~4, 505-515 (1999; Zbl 0919.49009)] that brings Clarke's derivative and fixed point theory into a joint framework. The authors, based on their former investigations, e.g., \textit{J. L. Li} [Far East J. Math. Sci., Spec. Vol., Part III, 299-312 (1999; Zbl 0985.47047)], establish further generalizations and incorporate some new ideas. One of the main results, Theorem 1 offers a fixed point theorem where no explicit continuity assumptions are made on the inward map considered. Variational inequalities involving Clarke's generalized derivative and a generalization of the main result of \textit{G. Kassay} and \textit{Zs. Páles} [loc. cit.] involving precoderivative instead of Clarke's generalized gradient are also obtained.