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The Radius of Convexity of Partial Sums of Convex Functions in One Direction

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Abstract

In this paper, we show that every section of function in a family of convex function in one direction in the open unit disk are convex in \({\mathbb {D}}_{1{/}2}=\{z\in {\mathbb {C}}: |z|<1{/}2\}\). The radius 1/2 is best possible.

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Authors and Affiliations

  1. Central University of Rajasthan, Dist-Ajmer, Bandarsindri, Kishangarh, Rajasthan, 305817, India

    Sudhananda Maharana & Jugal K. Prajapat

  2. University of Victoria, Victoria, BC, V8W 3R4, Canada

    Hari M. Srivastava

Authors
  1. Sudhananda Maharana
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  2. Jugal K. Prajapat
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  3. Hari M. Srivastava
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Correspondence to Jugal K. Prajapat.

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Maharana, S., Prajapat, J.K. & Srivastava, H.M. The Radius of Convexity of Partial Sums of Convex Functions in One Direction. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 87, 215–219 (2017). https://doi.org/10.1007/s40010-017-0348-7

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  • DOI: https://doi.org/10.1007/s40010-017-0348-7

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