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Convexity of Polynomials Using Positivity of Trigonometric Sums

  • Priyanka SangalEmail author
  • A. Swaminathan
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Positivity of trigonometric polynomials is of interest for more than a century because of its applications. In this work, we use positivity of trigonometric sine and cosine sums to find the convexity of a polynomial \(f(z)=\displaystyle \sum _{k=1}^n a_kz^k\). Further, we also investigate the radius of convexity r such that \(f(\mathbb {D}_{\rho })\) is convex where \(\mathbb {D}_{\rho }=\{z;|z|\leq \rho ,\, 0<\rho <1\}\).

Notes

Acknowledgements

The first author is thankful to the Council of Scientific and Industrial Research, India (grant code: 09/143(0827)/2013-EMR-1) for financial support to carry out the above research work.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Indian Institute of Technology RoorkeeRoorkeeIndia

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