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The goal of this paper is to establish a general fixed point theorem forcompact single-valued continuous mapping in Hausdorff p-vector spaces, and thefixed point theorem for upper semicontinuous set-valued mappings in Hausdorfflocally p-convex for p in (0, 1]. These new results provide an answer toSchauder conjecture in the affirmative under the setting of general p-vectorspaces for compact single-valued continuous, and also give the fixed pointtheorems for upper semicontinuous set-valued mappings defined on s-convexsubsets in Hausdorff locally p-convex spaces, which would be fundamental fornonlinear functional analysis in mathematics, where s,p in (0.1].

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