On the positivity of certain trigonometric sums and their applications

DOI10.1016/j.camwa.2011.09.037zbMath1236.42002OpenAlexW2048597525MaRDI QIDQ2429028

Anbhu Swaminathan, Saiful Rahman Mondal

Publication date: 22 April 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.09.037

zbMATH Keywords

Cesàro meansclose-to-convex functionsstarlike functionspositive trigonometric sum

Mathematics Subject Classification ID

Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (9)

Coefficient conditions for starlikeness of nonnegative order ⋮ Starlikeness of Gaussian hypergeometric functions using positivity techniques ⋮ On the study of trigonometric polynomials using strum sequence ⋮ Classes of Nonnegative Sine Polynomials ⋮ Geometric properties of Cesàro averaging operators ⋮ Fekete-Szegő problem for a certain subclass of close-to-convex functions ⋮ A refinement of Vietoris’ inequality for cosine polynomials ⋮ On generalized Cesàro stable functions ⋮ Certain geometric properties of Mittag-Leffler functions

Cites Work

• On a monotonic trigonometric sum
• On the order of starlikeness of the shifted Gauss hypergeometric function
• A class of positive trigonometric sums
• Geometric properties of the Cesàro means
• On a conjecture for trigonometric sums and starlike functions
• Extensions of Vietoris's inequalities I
• Positive Gegenbauer polynomial sums and applications to starlike functions
• Nonnegative sums of cosine, ultraspherical and Jacobi polynomials
• An extension of Vietoris's inequalities
• Positivity and boundedness of trigonometric sums
• Applications of a Convolution Theorem to Jacobi Polynomials
• New Criteria for Univalent Functions
• Successive Coefficients of Univalent Functions
• Positivity of some basic cosine sums
• Coefficient conditions for starlike functions
• Examples of trigonometric series with non-negative partial sums
• Shorter Notes: On a Positive Trigonometric Sum
• Some Positive Trigonometric Sums
• A NEW REFINEMENT OF YOUNG'S INEQUALITY
• Power series with multiply monotonic coefficients
• Two theorems on schlicht functions
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