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arXiv · 2506.14392

Higher Order Approximation of Continuous Functions by a Modified Meyer-K\"{o}nig and Zeller-Type Operator

Ivan Gadjev·Parvan Parvanov·Rumen Uluchev
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Abstract

A new Goodman-Sharma type modification of the Meyer-K\"{o}nig and Zeller operator for approximation of bounded continuous functions on [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-K\"{o}nig and Zeller type operator investigated by Ivanov and Parvanov in 2012.

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Ivan Gadjev, Parvan Parvanov, Rumen Uluchev. 2025-06-17. Higher Order Approximation of Continuous Functions by a Modified Meyer-K\"{o}nig and Zeller-Type Operator. https://arxiv.org/abs/2506.14392

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