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<p>This study introduces the development of wavelet-enhanced King-type Baskakov operators that preserve quadratic test functions. We get explicit formulas for the moments of these operators and demonstrate approximation results by Korovkin-type theorems. The rate of convergence is measured using the modulus of continuity, Lipschitz spaces, and statistical approximation, illustrating improved convergence characteristics. Quantitative error boundaries are established by direct approximation theorems, with numerical validation demonstrating a 20–50% reduction in error for oscillatory functions.</p>

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Quadratic function preserving wavelet type Baskakov operators for enhanced function approximation

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Mohammad Ayman-Mursaleen

摘要

This study introduces the development of wavelet-enhanced King-type Baskakov operators that preserve quadratic test functions. We get explicit formulas for the moments of these operators and demonstrate approximation results by Korovkin-type theorems. The rate of convergence is measured using the modulus of continuity, Lipschitz spaces, and statistical approximation, illustrating improved convergence characteristics. Quantitative error boundaries are established by direct approximation theorems, with numerical validation demonstrating a 20–50% reduction in error for oscillatory functions.