Continuous Selection Theorems in Generalized Convex Spaces

Continuous selections and fixed points of multi-valued mappings on noncompact or nonmetrizable spaces

“…If the index set I is a singleton, then Theorem 4.2 reduces to the following corollary, which provides a partial solution to a conjecture of Wu [15]. Finally we remark that in case I is a singleton, Theorem 4.1 provides a different result from [12,Theorem 3].…”

“…Later, Yannelis and N. D. Prabhakar [17], Ben-ElMechaiekh [2,3], Ding, Kim and Tan [8], Horvath [11], Wu [16,15], Park [12,13], and many others, established several continuous selection theorems with applications. We note that in all the continuous selection theorems studied by the above authors, the multi-valued maps are defined on a compact or paracompact space.…”

Coincidence theorem for admissible set-valued mappings and its applications in FC-spaces

“…We emphasis that major examples of F C-spaces are convex subsets of topological vector spaces, Lassonde's convex spaces in [10], C-spaces (or H-spaces) due to Horvath in [7], G-convex spaces due to Park and Kim in [13,14] and many other topological spaces with abstract convexity structures (see [13,14]). …”

Applications of some basic theorems in the KKM theory

“…The following extension of the Fan-Browder fixed point theorem to G-convex spaces is well known. For instance, it is a particular case of Theorem 3.3 and [ [26], Theorem 3].…”