Continuous Selection Theorems and Fixed Point Theorems for Fuzzy Mappings in FC-Spaces

Continuous selection theorem plays a key role in nonlinear problems arising in mathematics and applied science. Michael (1956) firstly established a famous continuous selection theorem. Browder (1968) proved a continuous selection theorem under the framework of para compact topological vector spaces. Since then, many authors have established continuous selection theorems under various assumptions in topological vector spaces or abstract topological spaces with generalized convex structure and have given applications in many different fields. By using the unity partition technique, this paper establishes some continuous selection theorems for fuzzy mappings in FC-spaces. Furthermore, as applications, some fixed point theorems for fuzzy mappings in FC-spaces are obtained. Our results generalize and improve the corresponding results in the recently existing literatures.