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June 14, 2026Demonstratio MathematicaOpen Access

Sharper upper bounds on maximum modulus for rational functions

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Authors

RTRanaranjan ThoudamRSRobinson SoraisamBCBarchand Chanam

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Overview

Randomized trial demonstrates enhanced estimates for maximum modulus of rational functions, implying better understandings of their behavior.

Key Points

  • The aim is to derive sharper upper bounds for the maximum modulus of rational functions, strengthening previous results.
  • Developed new inequality as a reverse analogue to Varga’s inequality for rational functions.
  • Refined Ankeny-Rivlin inequality by establishing sharper estimates for rational functions.
  • Utilized numerical examples through WOLFRAM MATHEMATICA to validate results.
  • Derived a new inequality that provides more precise upper bounds than traditional estimates.
  • Established stronger results for |r(γz)| with γ ≥ 1, enhancing understanding of rational function behavior.
  • Numerical examples demonstrate the superiority of the new estimates graphically and quantitatively.

Cite This Study

Thoudam et al. (2026) studied this question.

synapsesocial.com/papers/6a2e45d5b1cc60ccdea8ac4ehttps://doi.org/10.1515/dema-2025-0249
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