Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros

Abstract Two short proofs of a recently proposed intermediate value theorem for simplices are given. The obtained proofs are based on Sperner covering principles. Furthermore, this intermediate value theorem is applied for the localization and approximation of fixed points and zeros of continuous mappings using a simplicial subdivision of a simplex. Also, a theorem for the existence of a Sperner simplex (panchromatic simplex) in the considered simplicial subdivision is proved. In addition, an error estimate is presented.