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<p>In this present paper, we introduce Riemann-Liouville fractional type Schurer operators and its approximation properties. Firstly, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin type theorem and modulus of continuity for the space of univariate continuous functions and bivariate continuous functions in their sections. In continuation, local and global approximation properties are studied in terms of first and second order modulus of smoothness, Peetre’s <i>K</i>-functional and weight functions in various functional spaces. In subsequent section, we present approximation results for bivariate sequence of operators.</p>

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Novel fractional Schurer type operators with explicit error bounds and applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月15日

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  • Tripuresh Mishra,
  • Karunesh Kumar Singh,
  • Mohammad Ayman-Mursaleen,
  • Nadeem Rao

摘要

In this present paper, we introduce Riemann-Liouville fractional type Schurer operators and its approximation properties. Firstly, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin type theorem and modulus of continuity for the space of univariate continuous functions and bivariate continuous functions in their sections. In continuation, local and global approximation properties are studied in terms of first and second order modulus of smoothness, Peetre’s K-functional and weight functions in various functional spaces. In subsequent section, we present approximation results for bivariate sequence of operators.