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Stable Functions and Extension of Vietoris’ Theorem

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Abstract

In this work, using subordination results for the Cesáro sum of certain analytic functions, a concept called Cesáro stable is given and two conjectures in this direction are also proposed. Using an extension of Vietoris’ theorem on positivity of cosine sums, some results on positivity of cosine and sine sums are obtained. These results are useful in discussing some particular cases of the proposed conjectures.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Roorkee, 247 667, Uttarakhand, India

    Saiful R. Mondal & A. Swaminathan

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  1. Saiful R. Mondal
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  2. A. Swaminathan
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Correspondence to A. Swaminathan.

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S. R. Mondal was supported by UGC, New Delhi through a research fellowship.

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Mondal, S.R., Swaminathan, A. Stable Functions and Extension of Vietoris’ Theorem. Results. Math. 62, 33–51 (2012). https://doi.org/10.1007/s00025-011-0127-8

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  • DOI: https://doi.org/10.1007/s00025-011-0127-8

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