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Approximation by -Lupaş-Schurer-Kantorovich operators.

Kadir Kanat1, Melek Sofyalıoğlu1

  • 1Ankara Hacı Bayram Veli University Polatlı Faculty of Science and Arts, Ankara, Turkey.

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|October 27, 2018
PubMed
Summary

This study introduces novel q-analogue Kantorovich type Lupaş-Schurer operators, demonstrating their approximation capabilities using q-Jackson integrals and numerical methods.

Keywords:
Korovkin’s approximation theoremLocal approximationLupaş operatorsRate of convergence

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Area of Science:

  • Mathematical Analysis
  • Approximation Theory
  • Numerical Analysis

Background:

  • Lupaş-Schurer operators are significant in approximation theory.
  • q-Analogue operators extend classical operators to a more general framework.
  • Understanding convergence rates is crucial for practical applications.

Purpose of the Study:

  • To define and analyze the q-analogue of Kantorovich type Lupaş-Schurer operators.
  • To estimate the rate of convergence for these new operators.
  • To compare their approximation performance with existing operators.

Main Methods:

  • Utilizing the q-Jackson integral for operator construction.
  • Employing the modulus of continuity and Peetre's K-functionals for convergence analysis.
  • Implementing a Matlab algorithm for numerical illustration and comparison.

Main Results:

  • The q-analogue Kantorovich type Lupaş-Schurer operators were successfully constructed.
  • Rates of convergence were established using Lipschitz class functions and K-functionals.
  • Numerical results demonstrated the approximation behavior and compared it with q-Lupaş-Schurer operators.

Conclusions:

  • The q-analogue Kantorovich type Lupaş-Schurer operators provide a valuable tool for approximation.
  • The theoretical convergence estimates are supported by numerical findings.
  • This work contributes to the field of q-analogue approximation theory.