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A generalized Dunkl type modifications of Phillips operators.

M Nasiruzzaman1,2, Nadeem Rao3

  • 11Department of Computer Science & Engineering (SEST), Jamia Hamdard, New Delhi, India.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary

This study explores the convergence of Lebesgue measurable functions using a Dunkl generalization of Phillips operators. Researchers investigated qualitative results in Korovkin spaces to enhance uniform convergence.

Keywords:
Dunkl analogueGeneralization of exponential functionGenerating functionsKorovkin type theoremModulus of continuityOrder of convergenceSzász operator

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Area of Science:

  • Mathematical Analysis
  • Approximation Theory

Background:

  • Lebesgue measurable functions are fundamental in real analysis.
  • Szász-type operators and Phillips operators are established tools for function approximation.
  • Understanding convergence properties is crucial for developing new approximation methods.

Purpose of the Study:

  • To introduce and analyze a Dunkl generalization of Szász-type operators, specifically Phillips operators.
  • To investigate the uniform convergence of these generalized Phillips operators.
  • To explore the qualitative behavior of these operators within Korovkin and weighted Korovkin spaces.

Main Methods:

  • Construction of a Dunkl generalization of Phillips operators.
  • Application of Korovkin-type theorems for approximation operators.
  • Analysis of uniform convergence in weighted function spaces.

Main Results:

  • Establishment of convergence theorems for the Dunkl generalized Phillips operators.
  • Demonstration of improved uniform convergence properties compared to classical operators.
  • Characterization of the approximation behavior in specific function spaces.

Conclusions:

  • The Dunkl generalization of Phillips operators provides a powerful tool for approximating Lebesgue measurable functions.
  • The study offers new insights into the convergence rates and qualitative properties of these operators.
  • The findings contribute to the field of approximation theory, particularly in the context of generalized operators.