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Approximation and Computation pp 157–182Cite as

Positive Trigonometric Sums and Starlike Functions

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 42))

Abstract

We give a systematic account of new results on positive trigonometric sums. Applications in the context of geometric function theory are given. Our work is related to recent investigations concerning sharpening and generalizations of the celebrated Vietoris’ inequalities. Far-reaching extensions and results on starlike functions are obtained. New positive sums of Gegenbauer polynomials are also presented. We survey some recent results, give new and simpler proofs, and present further generalizations and extensions. We also pose and discuss some challenging conjectures.

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Acknowledgements

This research was supported by a grant from the Leventis Foundation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, 20537, 1678, Nicosia, CYPRUS

    Stamatis Koumandos

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  1. Stamatis Koumandos
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Correspondence to Stamatis Koumandos .

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Editors and Affiliations

  1. Dept. Computer Science, Purdue University, N. University Street 305, West Lafayette, 47907-2107, Indiana, USA

    Walter Gautschi

  2. Dipto. Matematica, Università Basilicata, Contrada Macchia Romana, Potenza, 85100, Italy

    Giuseppe Mastroianni

  3. Zagoras Street 4, Athens, 151 25, Greece

    Themistocles M. Rassias

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Dedicated to Gradimir V. Milovanović on the occasion of his 60-th anniversary

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Koumandos, S. (2010). Positive Trigonometric Sums and Starlike Functions. In: Gautschi, W., Mastroianni, G., Rassias, T. (eds) Approximation and Computation. Springer Optimization and Its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6594-3_12

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