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.


49J27 Existence theories for problems in abstract spaces
47H04 Set-valued operators
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
90C48 Programming in abstract spaces
Full Text: DOI


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