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On Better Approximation Order for the Nonlinear q-Bernstein Operator of Maximum Product Kind

Sezin Çit, Ogün Doğru

Abstract

Nonlinear q-Bernstein operator of max-product kind was introduced and its approximation order was examined, and the order of approximation was found to be by Duman in. In this paper, we obtained a better order of approximation for this operator.

On Better Approximation Order for the Nonlinear q-Bernstein Operator of Maximum Product Kind

Abstract

Nonlinear q-Bernstein operator of max-product kind was introduced and its approximation order was examined, and the order of approximation was found to be by Duman in. In this paper, we obtained a better order of approximation for this operator.
Paper Structure (5 sections, 8 theorems, 64 equations)

This paper contains 5 sections, 8 theorems, 64 equations.

Table of Contents

  1. Introduction
  2. Construction of the Operators
  3. Auxiliary Results
  4. Approximation Results
  5. $A$-Statistical Approximation

Key Result

Corollary 2.1

q bernstein For all $f\in C_{+}\left[ 0,1\right] ,$$n\in \mathbb{N},$$x\in \left[ 0,1\right]$ and $q\in \left( 0,1\right)$ we have where

Theorems & Definitions (11)

  • Corollary 2.1
  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • Theorem 4.1
  • proof
  • Corollary 4.1
  • Theorem 5.1
  • ...and 1 more