Abstract
The classical Markov (1889) and Bernstein (1912) inequalities and corresponding extremal problems were generalized for various domains, various norms and for various subclasses for polynomials, both algebraic and trigonometric. Beside some classical results in uniform norm, we give a short account of L r inequalities of Markov type for algebraic polynomials, with a special attention to the case r = 2. We also study extremal problems of Markov’s type
, where P n is the class of all algebraic polynomials of degree at most n, dλ(t) = w(t)dt is a nonnegative measure corresponding to the classical orthogonal polynomials, A ∈ P 2, and D m is a differential operator defined by
.
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Milovanović, G.V. (1999). Extremal Problems and Inequalities of Markov-Bernstein Type for Polynomials. In: Rassias, T.M., Srivastava, H.M. (eds) Analytic and Geometric Inequalities and Applications. Mathematics and Its Applications, vol 478. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4577-0_15
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DOI: https://doi.org/10.1007/978-94-011-4577-0_15
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