Fixed Point Theorems for Upper Semicontinuous Set-valued Mappings in p-Vector Spaces

Abstract

The goal of this paper is to establish a general fixed point theorem for upper semicontinuous set-values mappings in p-vector spaces (p∈(0, 1]), which include topological vector spaces as a special class. These new results provide an answer to Schauder conjecture in the affirmative under the setting of p-vector spaces for set-valued mappings, which would be fundamental for nonlinear functional analysis in mathematics. AMS Classification: 47H04, 47H10, 46A16, 46A55, 49J27, 49J35, 52A07, 54C60, 54H25, 55M20