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Approximation and error estimation by modified Păltănea operators associating Gould–Hopper 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 this article, we present a generalization of Păltănea operators associating Gould–Hopper polynomials. We obtain approximation properties of our operators by means of the universal Korovkin’s theorem and examine convergence properties by applying modulus of continuity, the second order modulus of smoothness and Peetre’s K-functional and also demonstrated the convergence of these operators graphically for particular functions. Voronovskaja type asymptotic formula is also established. Further, we estimate the rate of point-wise convergence of these operators for functions with derivative of bounded variation. The convergence of these operators are also discussed in weighted spaces of functions on the positive semi-axis and estimate the approximation with the help of weighted modulus of continuity. Lastly, we computed errors in approximating different functions by defined operators and also shown these results graphically. All the graphics and computation of errors are done with the help of MATLAB.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under Grant number R.G.P. 1/13/40.

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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

    Shagufta Rahman & M. Mursaleen

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

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Ansari, K.J., Rahman, S. & Mursaleen, M. Approximation and error estimation by modified Păltănea operators associating Gould–Hopper polynomials. RACSAM 113, 2827–2851 (2019). https://doi.org/10.1007/s13398-019-00661-0

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