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L-P-Analogues of Bernstein and Markov Inequalities


Muñoz-Fernández, Gustavo A. and Sánchez, V.M. and Seoane-Sepúlveda, Juan Benigno (2011) L-P-Analogues of Bernstein and Markov Inequalities. Mathematical Inequalities & Applications, 14 (1). pp. 135-145. ISSN 1331-4343

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Let parallel to . parallel to(infinity) denote the sup norm on [-1,1]. If x is an element of [-1,1] is fixed and M-m,M-n(x) is the best constant in vertical bar p'(x)vertical bar <= M-m,M-n(x)parallel to p parallel to(infinity), for all trinomials p of the form p(x) = ax(m) + bx(n) + c with a, b, c is an element of R, then the exact value of M-m,M-n(x) is known for large families of pairs (m,n) is an element of N-2. Here we consider the same problem for L-p-norms.

Item Type:Article
Uncontrolled Keywords:Bernstein and Markov type inequality; trinomial
Subjects:Sciences > Mathematics > Functions
ID Code:16897

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