Integral estimates for a class Bn of operators
DOI:
https://doi.org/10.24193/subbmath.2018.2.02Keywords:
B-Operator, polynomial inequalities, integral estimates.Abstract
Let Pn be the class of polynomials of degree at most n. Rahman introduced a class Bn of operators B that map Pn into itself. In this paper, we establish certain integral estimates concerning B-operator, and thereby obtain generalizations as well as improvements of some well known inequalities for polynomials.
Mathematics Subject Classification (2010): 26D10, 41A17.
References
Ankeny, N.C., Rivlin, T.J., On a Theorem of S. Bernstein, Pacific J. Math., 5(1955), 849–852.
Aresto¨v, V.V., On integral inequalities for trigonometric polynomials and their derivatives, Izv. Akad. Nauk. SSSR. Ser. Mat., 45(1981), 3-22 (in Russian); Math. USSR-Izv., 18(1982), 1–17 (in English).
Aziz, A., Dawood, Q.M., Inequalities for a polynomial and its derivative, J. Approx. Theory, 54(1988), 306-313.
Aziz, A., Rather, N.A., Some compact generalizations of Zygmund-type inequalities for polynomials, Nonlinear Studies, 6(1999), 241–255.
Aziz, A., Shah, W.M., Lp inequalities for polynomials with restricted zeros, Glasnik Matematicki, 57(2002), 73–81.
Bernstein, S., Sur la limitation des d´eriv´ees des polynomes, C. R. Acad. Sci. Paris, 190(1930), 338-340.
Boas Jr., R.P., Rahman, Q.I., Lp inequalities for polynomials and entire functions, Arch. Rational Mech. Anal., 11(1962), 34–39.
de Bruijn, N.G., Inequalities concerning polynomials in the complex domain, Neder. Akad. Wetensch. Proc., 50(1947), 1265–1272.
Govil, N.K., Liman, A., Shah, W.M., Some inequalities concerning derivative and max- imum modulus of polynomials, Aust. J. Math. Anal. Appl., 8(2011), 1–8.
Hardy, G.H., The mean value of the modulus of an analytic function, Proc. London. Math. Soc., 14(1915), 269–277.
Lax, P.D., Proof of a conjecture of P. Erd¨os on the derivative of a polynomial, Bull. Amer. Math. Soc., 50(1944), 509–513.
Marden, M., Geometry of polynomials, Second Ed., Math. Surveys, no. 3, Amer. Math. Pro., R.I., 1996.
Rahman, Q.I., Schmeisser, G., Lp inequalities for polynomials, J. Approx. Theory, 53(1988), 26–32.
Rahman, Q.I., Schmeisser, G., Analytic Theory of Polynomials, Oxford Univ. Press, 2002.
Shah, W.M., Liman, A., An operator preserving inequalities between polynomials, J. Inequal. Pure Appl. Math., 9(2009), 1–12.
Shah, W.M., Liman, A., Integral estimates for the family of B-operators, Operators and Matrices, 5(2011), 79–87.
Wali, S.L., Shah, W.M., Liman, A., Inequalities Concerning B-Operators, Probl. Anal. Issues Anal. 23(5)(2016), 55-72.
Zygmund, A., A remark on conjugate series, Proc. London Math. Soc., 34(2)(1932), 392–400.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
