Durrmeyer variant of Apostol-Genocchi-Baskakov operators (original) (raw)

Abstract

We study the approximation behavior of the Durrmeyer form of Apostol-Genocchi polynomials with Baskakov type operators including K-functional and second-order modulus of smoothness, Lipschitz space and find the rate of convergence for continuous functions whose derivative satisfies the condition of bounded variation. In the last section, we estimate weighted approximation behavior for these operators.

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  1. The study establishes the approximation behavior of Durrmeyer Apostol-Genocchi operators with Baskakov type operators.
  2. The paper evaluates convergence rates for continuous functions with bounded variation derivatives.
  3. It introduces K-functional and second-order modulus of smoothness for analyzing operator behavior.
  4. Convergence results are derived using the Bohmann-Korovkin theorem and modulus of continuity.
  5. Estimates for weighted approximation behavior are provided for the discussed operators.

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