Foundations of the KKM Theory on Generalized Convex Spaces
نویسندگان
چکیده
منابع مشابه
Generalized Kkm Maps on Generalized Convex Spaces
In the present paper, we extend known KKM theorems and matching theorems for generalized KKM maps to G-convex spaces. From these results, we deduce generalized versions of main results of Kassay and Kolumbán [KK] and some others.
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Various types of φA-spaces (X,D; {φA}A∈〈D〉) are simply G-convex spaces. Various types of generalized KKM maps on φA-spaces are simply KKM maps on G-convex spaces. Therefore, our G-convex space theory can be applied to various types of φAspaces. As such examples, we obtain KKM type theorems and a very general fixed point theorem on φA-spaces. RESUMEN Varios tipos de φA-espacios (X,D; {φA}A∈〈D〉) ...
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In the present paper, slightly modifying the topological KKM Theorem of Park and Kim (1996), we obtain a new existence theorem for generalized vector equilibrium problems related to an admissible multifunction. We work here under the general framework of G-convex space which does not have any linear structure. Also, we give applications to greatest element, fixed point and vector saddle point p...
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A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones in G-convex spaces and φA-spaces X,D; {φA}A∈〈D〉 . Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized an...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1997
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5388