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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
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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
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. (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)
Dragomir, S.S. (2004) Discrete inequalities of the Cauchy-Bunyakovsky-Schwarz type. N.Y: Nova Science Publishers Inc
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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