×

zbMATH — the first resource for mathematics

Analogs of the Markov and Schaeffer-Duffin inequalities for convex bodies. (English. Russian original) Zbl 1009.46028
Math. Notes 68, No. 1, 130-134 (2000); translation from Mat. Zametki 68, No. 1, 146-150 (2000).
There are presented estimations for Fréchet derivatives of polynomial mappings of a real Banach space \(X\) into \(\mathbb{R}\) on some convex bodies of \(X\). Results are expressed in dependence on the degree \(n\) of the polynomial mapping \( P_{n}:X\rightarrow \mathbb{R}\) and on certain geometrical characterizations of the corresponding convex body \(V\subset X\). These results generalize inequalities of A. C. Schaeffer and R. I. Duffin [Bull. Am. Math. Soc. 44, 289-297 (1938; Zbl 0018.39503)].

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
52A40 Inequalities and extremum problems involving convexity in convex geometry
46T20 Continuous and differentiable maps in nonlinear functional analysis
46G25 (Spaces of) multilinear mappings, polynomials
PDF BibTeX XML Cite