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Some existence theorems in nonlinear analysis for mappings on GFC-spaces and applications. (English) Zbl 1188.49006
Summary: We establish a maximal element theorem, an intersection theorem and a coincidence-point theorem in product GFC-spaces. As examples of wide ranges of applications, we first deduce sufficient conditions for the existence of a solution of a mixed system of inclusions. Then using this we obtain existence results for systems of vector quasi-optimization problems and for multiobjective mathematical programs constrained by systems of inclusions. Our results are shown to improve and include recent ones in the literature.
MSC:
49J27Optimal control problems in abstract spaces (existence)
47H04Set-valued operators
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54H25Fixed-point and coincidence theorems in topological spaces
90C48Programming in abstract spaces