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A basic problem of [Formula: see text]-Bernstein-type operators.

Qing-Bo Cai1, Xiao-Wei Xu2

  • 1School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, China.

Journal of Inequalities and Applications
|July 7, 2017
PubMed
Summary
This summary is machine-generated.

This study refines convergence theorems for q-analogue Bernstein-type operators. We identify specific q-integer conditions ensuring convergence, correcting prior literature on these mathematical operators.

Keywords:
Bernstein-type approximation[Formula: see text]-integerconvergence theoremequivalent condition

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Area of Science:

  • Mathematical Analysis
  • Approximation Theory

Background:

  • Bernstein-type operators are fundamental in approximation theory.
  • Convergence properties of their q-analogues are an active research area.
  • Existing literature contains inaccuracies regarding these operators.

Purpose of the Study:

  • To elaborate on a core problem concerning the convergence theorem of q-analogue Bernstein-type operators.
  • To derive precise conditions for the convergence of these operators.
  • To correct and improve upon existing results in the literature.

Main Methods:

  • Utilizing classical analysis techniques.
  • Deriving exact conditions for q-integers.
  • Analyzing the convergence behavior under specific constraints.

Main Results:

  • An exact class of q-integers satisfying specific conditions was determined.
  • The convergence theorem for q-analogue Bernstein-type operators was elaborated.
  • An erratum to recent literature was provided.

Conclusions:

  • The derived conditions precisely define the convergence of q-analogue Bernstein-type operators.
  • This work corrects and enhances the understanding of these mathematical operators.
  • The findings contribute to the field of approximation theory and mathematical analysis.