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Coincidence and fixed point theorems with applications. (English) Zbl 1029.54047

Summary: We first establish a coincidence theorem under noncompact settings. Then we derive some fixed point theorems for a family of functions. We apply our fixed point theorem to study intersection problems for sets with convex sections and obtain a social equilibrium existence theorem.

We also introduce a concept quasivariational inequalities and prove an existence result for a solution to such a system.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
91B50General equilibrium theory in economics
47H10Fixed point theorems for nonlinear operators on topological linear spaces
49J40Variational methods including variational inequalities
49J35Minimax problems (existence)
47J20Inequalities involving nonlinear operators
47N10Applications of operator theory in optimization, convex analysis, programming, economics