Positive Trigonometric Sums and Starlike Functions

Stamatis Koumandos ()
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Stamatis Koumandos: University of Cyprus

A chapter in Approximation and Computation, 2010, pp 157-182 from Springer

Abstract: 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.

Keywords: Harmonic Function; Trigonometric Series; Starlike Function; Geometric Function Theory; Ultraspherical Polynomial (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-6594-3_12

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DOI: 10.1007/978-1-4419-6594-3_12

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