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2015, vol. 19, iss. 2, pp. 125-140
Further inequalities for power series with nonnegative coefficients via a reverse of Jensen inequality
Mathematics, College of Engineering & Science, Victoria University, Melbourne City, Australia + School of Computational & Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa

emailsever.dragomir@vu.edu.au
Keywords: power series; Jensen's inequality; reverse of Jensen's inequality
Abstract
Some inequalities for power series with nonnegative coefficients via a new reverse of Jensen inequality are given. Applications for some fundamental functions defined by power series are also provided.
References
Cerone, P., Dragomir, S.S. (2007) Some applications of de Bruijn's inequality for power series. Integral Transforms and Special Functions, 18(6): 387-396
Cerone, P., Dragomir, S.S. (2007) A refinement of the Grüss inequality and applications. Tamkang J. Math, 38, No. 1, pp. 37-49, Preprint RGMIA Res. Rep. Coll., 5 (2) (2002), Art. 14 [http://rgmia.org/papers/v5n2/RGIApp.pdf]
Dragomir, S.S. (2013) Some reverses of the jensen inequality with applications. Bulletin of the Australian Mathematical Society, 87(02): 177-194
Dragomir, S.S. (2004) Discrete inequalities of the Cauchy-Bunyakovsky-Schwarz type. N.Y: Nova Science Publishers Inc
Dragomir, S.S. (2014) Inequalities for power series with nonnegative coefficients via a reverse of Jensen inequality. RGMIA Res. Rep. Coll, 17, Art. 47, http://rgmia.org/papers/v17/v17a47.pdf
Dragomir, S.S., Ionescu, N.M. (1994) Some converse of Jensen's inequality and applications. Rev. Anal. Numér. Théor. Approx, 23, no. 1, pp. 71-78, MR1325895 (96c:26012)
Ibrahim, A., Dragomir, S.S. (2011) Power series inequalities via Buzano's result and applications. Integral Transforms and Special Functions, 22(12): 867-878
Ibrahim, A., Dragomir, S.S. (2012) Power series inequalities via a refinement of the Schwarz inequality. Integral Transforms and Special Functions, 23(10): 769-781
Ibrahim, A., Dragomir, S.S. (2014) A Survey on Cauchy-Bunyakovsky-Schwarz Inequality for Power Series. in: Milovanović, Gradimir V.; Rassias, Michael Th. [ed.] Analytic Number Theory, Approximation Theory, and Special Functions, New York, NY: Springer Nature America, Inc, str. 247-295
Ibrahim, A., Dragomir, S.S., Darus, M. (2013) Some inequalities for power series with applications. Integral Transforms and Special Functions, 24(5): 364-376
Ibrahim, A., Dragomir, S.S., Darus, M. (2013) Power series inequalities related to Young's inequality and applications. Integral Transforms and Special Functions, 24(9): 700-714
Ibrahim, A., Dragomir, S.S., Darus, M. (2013) Power series inequalities via Young’s inequality with applications. Journal of Inequalities and Applications, 2013(1): 314
 

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article language: English
document type: unclassified
DOI: 10.5937/MatMor1502125S
published in SCIndeks: 25/03/2017

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