A Unified Fixed Point Theory in Generalized Convex Spaces
Authors:
Sehie Park
Affiliation:
(1) The National Academy of Sciences, Republic of Korea;(2) School of Mathematical Sciences, Seoul National University, Seoul, 151–747, Korea
Abstract:
Let be the class of ‘better’ admissible multimaps due to the author. We introduce new concepts of admissibility (in the sense of Klee) and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap infrom a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of Φ-spaces, sets of the Zima–Hadžić type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.