Approximation by Jakimovski–Leviatan operators of Durrmeyer type involving multiple Appell polynomials

  • Khursheed J. Ansari
  • M. Mursaleen
  • Shagufta Rahman
Original Paper


In the present paper, we introduce Jakimovski–Leviatan–Durrmeyer type operators involving multiple Appell polynomial. First, we investigate Korovkin type approximation theorem and rate of convergence by using usual modulus of continuity and class of Lipschitz function. Next, we study the convergence of these operators in weighted space of functions and estimate the approximation properties. We have also established Voronovskaja type asymptotic formula. Furthermore, we obtain statistical approximation properties of these operators with the help of universal Korovkin type statistical approximation theorem. Some graphical examples for the convergence of our operators towards some functions are given. At the end, we have computed error estimation as our numerical example.


Multiple Apple polynomial Durrmeyer operators Jakimovski–Leviatan operators Modulus of continuity Statistical approximation 

Mathematics Subject Classification

41A10 41A28 41A36 



The first author would like to express his gratitude to King Khalid University, Abha, Saudi Arabia for providing administrative and technical support.


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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  • Khursheed J. Ansari
    • 1
  • M. Mursaleen
    • 2
  • Shagufta Rahman
    • 2
  1. 1.Department of Mathematics, College of ScienceKing Khalid UniversityAbhaSaudi Arabia
  2. 2.Department of MathematicsAligarh Muslim UniversityAligarhIndia

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