On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser

• Autorzy: Qazi M. A.

Identyfikatory

DOI

10.4064/ba62-1-5

• Języki publikacji: EN

Abstrakty

EN

In this paper, a generalization of a result on the uniform best approximation of αcosnx+βsinnx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.

Słowa kluczowe

EN

uniform best approximation; trigonometric polynomials; functions of exponential type; polynomials; Visser’s inequality

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 1
• Strony: 43--48
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Qazi M. A.

• Department of Mathematics Tuskegee University Tuskegee, AL 36088, U.S.A.

Bibliografia

• [1] N. I. Akhiezer, Theory of Approximation, Frederick Ungar, New York, 1956.
• [2] A. S. Besicovitch, Almost Periodic Functions, Dover Publ., 1954.
• [3] R. P. Boas, Jr., Entire Functions, Academic Press, New York, 1954.
• [4] J. G. van der Corput and C. Visser, Inequalities concerning polynomials and trigonometric polynomials, Indag. Math. 8 (1946), 238–247.
• [5] Q. I. Rahman, Inequalities concerning polynomials and trigonometric polynomials, J. Math. Anal. Appl. 6 (1963), 303–324.
• [6] Q. I. Rahman and G. Schmeisser, Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002.
• [7] C. Visser, A simple proof of certain inequalities concerning polynomials, Indag. Math. 7 (1945), 81–86.