A well-known result of Chebyshev is that if pn ∊ Pn , (Pn is the set of polynomials of degree at most n) and
then an(pn), the leading coefficient of pn , satisfies
with equality holding only for pn = ±Tn , where Tn is the Chebyshev polynomial of degree n. (See [6, p. 57].) This is an example of an extremal problem in which the norm of a given linear operator on Pn is sought. Another example is A. A. Markov's result that (1) implies that
There are also results for the linear functionals pn (k) (x 0), x 0 real, k = 1, … n – 1 ().
Suppose φ(x) ≧ 0 on [–1, 1] and (1) is generalized to
as suggested by Rahman  (polynomials with curved majorants), what can then be said about the analogue of (3) or similar extremal problems?