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For a function f defined on an interval [a, b] let ∥f∥ [a,b] := sup{|f(x)|: x ∈ [a,b]}. The principal result of this paper is the following Markov-type inequality for Muntz polynomials. Theorem. Let n > 1 be an integer. Let λ 0 , λ 1 ,...,λ n be n + 1 distinct real numbers. Let 0 < a < b. Then formula math. formula math. where the supremum is taken for all Q ∈ span{x λ 0,x λ 1,.., x λ n} (the span is the linear span over R).

The full Markov-Newman inequality for Müntz polynomials on positive intervals