New inequalities of CBS-type for power series of complex numbers

• Autorzy: Dragomir S. S.

Identyfikatory

DOI

10.1515/fascmath-2016-0015

• Języki publikacji: EN

Abstrakty

EN

Let [formula] be a function defned by power series with complex coefficients and convergent on the open disk D (0, R) C, R > 0. In this paper we show amongst other that, if α, z C are such that |α|, |α||z| < R, then [formula] where [formula]. Aplications for some fundamental functions defined by power series are also provided. be a function defned by power series with complex coefficients and convergent on the open disk D(0, R) C, R > 0. In this paper we show amongst other that, if α, z C are such that |α|, |α||z| < R, then [formula] where Applications for some fundamental functions defined by power series are also provided.

Słowa kluczowe

EN

power series; CBS-type inequalities

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2016
• Tom: Nr 57
• Strony: 37--51
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Dragomir S. S.

• Mathematics, College of Engineering & Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia
• School of Computer Science & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

Bibliografia

• [1] Cerone P., Dragomir S.S., Some applications of de Bruijn's inequality for power series, Integral Transform. Spec. Funct., 18(6), (2007), 387-396.
• [2] de Bruijn N.G., Problem 12, Wisk. Opgaven, 21(1960), 12-14.
• [3] Dragomir S.S., Discrete Inequalities of the Cauchy-Bunyakovsky-Schwarz Type, Nova Science Publishers Inc., N.Y., 2004.
• [4] Ibrahim A., Dragomir S.S., Power series inequalities via Buzano's result and applications, Integral Transform. Spec. Funct., 22(12), (2011), 867-878.
• [5] Ibrahim A., Dragomir S.S., Power series inequalities via a refinement of Schwarz inequality, Integral Transform. Spec. Funct., 23(10), (2012), 769-78.
• [6] Ibrahim A., Dragomir S.S., Darus M., Some inequalities for power series with applications, Integral Transform. Spec. Funct., 24(5), (2013), 364-376.
• [7] Ibrahim A., Dragomir S.S., A survey on Cauchy-Bunyakovsky-Schwarz inequality for power series, p. 247-p. 295, in G.V. Milovanović and M.Th. Rassias (eds.), Analytic Number Theory, Approximation Theory, and Special Functions, Springer, 2013. DOI 10.1007/978-1-4939-0258-3 10.
• [8] Mitrinović D.S., Pečarićѧ J.E., Fink A.M., Classical and New Inequalities in Analysis, Kluwer Academic Publishers, 1993.

Uwagi

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