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Closed convex hull of multivalent symmetric close-to-convex functions of order β with the Montel normalization

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Abstract

We obtain a one-to-one tranformation of the family of multivalent symmetric close-to-convex functions of order β, onto the family of multivalent symmetric close-to-convex functions of order β with the Montel normalization. Using this transformation we determine the closed convex hull and extreme points of the latter class for β≥1.

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Authors and Affiliations

  1. Department of Mathematics, Berhampur University, Berhampur-760007, Orissa, India

    A. K. Mishra

  2. Department of Statistics, Khallikote Autonomous College, Berhampur-760001, Ganjam, Orissa, India

    P. Sahu

Authors
  1. A. K. Mishra
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  2. P. Sahu
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Additional information

The present investigation is partially supported by National Board for Higher Mathematics, Department of Atomic Energy, Government of India under Grant No. 48/2/2003-R & D II.

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Mishra, A.K., Sahu, P. Closed convex hull of multivalent symmetric close-to-convex functions of order β with the Montel normalization. Rend. Circ. Mat. Palermo 56, 90–100 (2007). https://doi.org/10.1007/BF03031431

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  • DOI: https://doi.org/10.1007/BF03031431

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