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

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

    Khursheed J. Ansari

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen & Shagufta Rahman

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  1. Khursheed J. Ansari
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  2. M. Mursaleen
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  3. Shagufta Rahman
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Correspondence to Khursheed J. Ansari.

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Ansari, K.J., Mursaleen, M. & Rahman, S. Approximation by Jakimovski–Leviatan operators of Durrmeyer type involving multiple Appell polynomials. RACSAM 113, 1007–1024 (2019). https://doi.org/10.1007/s13398-018-0525-9

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  • DOI: https://doi.org/10.1007/s13398-018-0525-9

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