A refinement of Schwarz's lemma and its applications

• Autorzy: Jain V. K.

Identyfikatory

DOI

10.7862/rf.2016.5

• Języki publikacji: EN

Abstrakty

EN

By using the value of the second derivative of the function at 0, along with the values of the function and its first derivative at 0, we have obtained a refinement of well known Schwarz’s lemma and have used this refinement to obtain refinements, of Aziz and Rather’s inequalities [2004] for a polynomial of degree n having no zeros in |z| < k, (k ≥ 1).

Słowa kluczowe

EN

Schwarz lemma; polynomial; inequalities

PL

lemat Schwarza; wielomian; nierówność

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2016
• Tom: Vol. 39
• Strony: 69--80
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Jain V. K.

• Mathematics Department, I.I.T., Kharagpur - 721302, India

Bibliografia

• [1] A. Aziz, N.A. Rather, Some Zygmund type Lq inequalities for polynomials, J. Math. Anal. Appl. 289 (2004) 14-29.
• [2] E.T. Copson, An Introduction to the Theory of Functions of a Complex Variable, The English Language Book Society and Oxford University Press, Oxford, 1961.
• [3] N.K. Govil, Q.I. Rahman, Functions of exponential type not vanishing in a half plane and related polynomials, Trans. Amer. Math. Soc. 137 (1969) 501-517.
• [4] N.K. Govil, Q.I. Rahman, G. Schmeisser, On the derivative of a polynomial, Ill. J. Maths. 23 (1979) 319-329.
• [5] Z. Nehari, Conformal Mapping, 1st edition, McGraw-Hill, New York, 1952.
• [6] E.C. Titchmarsh, The Theory of Functions, The English Language Book Society and Oxford University Press, London, 1962.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).