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We present a constructive proof of Tychonoff's fixed point theorem in alocally convex space for sequentially locally non-constant functions, As acorollary to this theorem we also present Schauder's fixed point theorem in aBanach space for sequentially locally non-constant functions. We follow theBishop style constructive mathematics.

Constructive proofs of Tychonoff's and Schauder's fixed point theorems for sequentially locally non-constant functions