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On the rate of convergence for the q-Durrmeyer polynomials in complex domains

  • Ovgu Gurel EMAIL logo , Sofiya Ostrovska and Mehmet Turan
Published/Copyright: October 15, 2024
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 74 Issue 5

Abstract

The q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set 𝓓 ⊂ ℂ, the rate of convergence is O(qn) as n → ∞. The sharpness of the obtained result is demonstrated.

Keywords: q-integers; q-Durrmeyer operator; limit q-Durrmeyer operator; rate of convergence; analytic function
MSC 2010: 41A25; 30E10

Acknowledgement

The authors express their sincere gratitude to the anonymous referees for their thorough reading of the manuscript and beneficial comments.

  1. Communicated by Tomasz Natkaniec

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Received: 2024-01-11
Accepted: 2024-04-26
Published Online: 2024-10-15
Published in Print: 2024-10-28

© 2024 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2024-0092
Keywords for this article
q-integers; q-Durrmeyer operator; limit q-Durrmeyer operator; rate of convergence; analytic function

Articles in the same Issue

  1. On monoids of endomorphisms of a cycle graph
  2. The influence of separating cycles in drawings of K5 ∖ e in the join product with paths and cycles
  3. Completely hereditarily atomic OMLS
  4. New notes on the equation d(n) = d(φ(n)) and the inequality d(n) > d(φ(n))
  5. On the monogenity and Galois group of certain classes of polynomials
  6. Other fundamental systems of solutions of the differential equation (D2 – 2αD + α2 + ÎČ2)ny = 0, ÎČ â‰  0
  7. Characterization of continuous additive set-valued maps “modulo K” on finite dimensional linear spaces
  8. Hermite–Hadamard inequalities for Riemann–Liouville fractional integrals
  9. Global Mild Solutions For Hilfer Fractional Neutral Evolution Equation
  10. The discrete fractional Karamata theorem and its applications
  11. Complex Generalized Stancu-Schurer Operators
  12. New oscillatory criteria for third-order differential equations with mixed argument
  13. Cauchy problem for a loaded hyperbolic equation with the Bessel operator
  14. Liouville type theorem for a system of elliptic inequalities on weighted graphs without (p0)-condition
  15. On the rate of convergence for the q-Durrmeyer polynomials in complex domains
  16. Some fixed point theorems in generalized parametric metric spaces and applications to ordinary differential equations
  17. On the relation of Kannan contraction and Banach contraction
  18. Extropy and statistical features of dual generalized order statistics’ concomitants arising from the Sarmanov family
  19. Residual Inaccuracy Extropy and its properties
  20. Archimedean ℓ-groups with strong unit: cozero-sets and coincidence of types of ideals
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