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Some Rational Inequalities Inspired by Rahman’s Research

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Progress in Approximation Theory and Applicable Complex Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 117))

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Abstract

This paper describes three instances of our research activity in rational inequalities inspired by Professor Rahman’s research. The results include Bernstein-type inequalities for rational functions with prescribed poles, comparison inequalities for rational functions, and integral inequalities with prescribed poles and prescribed zeros.

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Notes

  1. 1.

    By “right formulation” we mean in the sense that when taking modulus inside the integration, the equality could be attained for some special cases - not every integral formula allows such sharp estimation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA

    Xin Li

  2. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA

    Ram Mohapatra

  3. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA

    Rajitha Ranasinghe

Authors
  1. Xin Li
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  2. Ram Mohapatra
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  3. Rajitha Ranasinghe
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Corresponding author

Correspondence to Ram Mohapatra .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Auburn University, Auburn, Alabama, USA

    Narendra Kumar Govil

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    Ram Mohapatra

  3. Department of Mathematics, Tuskegee University, Tuskegee, Alabama, USA

    Mohammed A. Qazi

  4. Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany

    Gerhard Schmeisser

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Li, X., Mohapatra, R., Ranasinghe, R. (2017). Some Rational Inequalities Inspired by Rahman’s Research. In: Govil, N., Mohapatra, R., Qazi, M., Schmeisser, G. (eds) Progress in Approximation Theory and Applicable Complex Analysis. Springer Optimization and Its Applications, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-49242-1_6

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