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

Ansari, Qamrul H.; Idzik, Adam; Yao, Jen-Chih

Topol. Methods Nonlinear Anal. 15, No. 1, 191-202 (2000).

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:

54H25	Fixed-point and coincidence theorems (topological aspects)
91B50	General equilibrium theory
47H10	Fixed-point theorems
49J40	Variational inequalities
49J35	Existence of solutions for minimax problems
47J20	Variational and other types of inequalities involving nonlinear operators (general)
47N10	Applications of operator theory in optimization, convex analysis, mathematical programming, economics