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<p>A Goodman-Sharma type modification of the Meyer-König and Zeller operator for approximation of continuous functions on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\([0,\,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em" /> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is presented. We estimate the approximation error of the proposed operator and prove direct and strong converse theorems with respect to a related K-functional. The operator is linear but not a positive one. However it benefits a better order of approximation compared to the Goodman-Sharma variant of Meyer-König and Zeller type operator investigated by Ivanov and Parvanov in 2012.</p>

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Higher Order Approximation of Continuous Functions by a Modified Meyer-König and Zeller-Type Operator

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Ivan Gadjev,
  • Parvan E. Parvanov,
  • Rumen Uluchev

摘要

A Goodman-Sharma type modification of the Meyer-König and Zeller operator for approximation of continuous functions on \([0,\,1)\) [ 0 , 1 ) is presented. We estimate the approximation error of the proposed operator and prove direct and strong converse theorems with respect to a related K-functional. The operator is linear but not a positive one. However it benefits a better order of approximation compared to the Goodman-Sharma variant of Meyer-König and Zeller type operator investigated by Ivanov and Parvanov in 2012.