An extremal property for Chebyshev polynomials (Q1201281)

Among the class of \(n\)th degree polynomials in the unit leading coefficient, Chebyshev polynomials possess the least deviation from zero on the interval \([-1,1]\) with certain norms. This result is carefully generalized here. The main conclusions are presented in the form of three theorems and three corollaries. Proofs of all the theorems are provided with the help of four lemmas. The results are of immense value and hold hope for further extensions.