On a conjecture for trigonometric sums and starlike functions

DOI10.1016/j.jat.2007.04.006zbMath1135.42001OpenAlexW2067437083WikidataQ123126277 ScholiaQ123126277MaRDI QIDQ2472363

Stamatis Koumandos, Stephan Ruscheweyh

Publication date: 21 February 2008

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2007.04.006

zbMATH Keywords

subordinationstarlike functionstrigonometric inequalitiespositive trigonometric sums

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Inequalities for sums, series and integrals (26D15) Inequalities for trigonometric functions and polynomials (26D05) Trigonometric polynomials, inequalities, extremal problems (42A05) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (19)

Some subordination involving polynomials induced by lower triangular matrices ⋮ Sharp estimates for various trigonometric sums ⋮ An extension of Vietoris's inequalities ⋮ Coefficient conditions for starlikeness of nonnegative order ⋮ Starlikeness of Gaussian hypergeometric functions using positivity techniques ⋮ A sharp inequality for a trigonometric sum ⋮ On the positivity of certain trigonometric sums and their applications ⋮ On the study of trigonometric polynomials using strum sequence ⋮ Stable functions of Janowski type ⋮ Complete monotonicity and related properties of some special functions ⋮ Stable functions and extension of Vietoris' theorem ⋮ Some completely monotonic functions of positive order ⋮ On a conjecture for trigonometric sums and starlike functions. II. ⋮ Monotonicity of some functions involving the gamma and psi functions ⋮ High precision computation of a constant in the theory of trigonometric series ⋮ A refinement of Vietoris' inequality for sine polynomials ⋮ On generalized Cesàro stable functions ⋮ Certain geometric properties of Mittag-Leffler functions ⋮ The zeros of certain Lommel functions

Cites Work

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• A class of positive trigonometric sums
• Linear operators between classes of prestarlike functions
• Stable functions and Vietoris' theorem
• Positive Gegenbauer polynomial sums and applications to starlike functions
• On the growth of univalent functions
• An extension of Vietoris's inequalities
• Monotonicity of some functions involving the gamma and psi functions
• Some Positive Trigonometric Sums

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