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Higher order Kantorovich operators based on inverse Pólya–Eggenberger distribution

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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 provide a higher order Kantorovich type integral operators based on inverse Pólya–Eggenberger distribution. We use the methods of finite differences to establish a link with the discrete operators. Also, we find the quantitative estimate for the difference of these operators with several other operators based on inverse Pólya–Eggenberger distribution. In the last section, we present the convergence of these operators to some functions in pictorial form.

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References

  1. Acu, A.M., Raşa, I.: New estimates for the differences of positive linear operators. Numer. Algorithms 73, 775–789 (2016)

    Article  MathSciNet  Google Scholar 

  2. Acu, A.M., Acar, T., Radu, V.A.: Approximation by modified \(U_n^\rho \) operators. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. RACSAM 113, 2715–2729 (2019). https://doi.org/10.1007/s13398-019-00655-y

  3. Acu, A.M., Hodiş, S., Raşa, I.: Estimates for the differences of certain positive linear operators. Mathematics 8(5), 798 (2020). https://doi.org/10.3390/math8050798

    Article  MATH  Google Scholar 

  4. Agrawal, P.N., Acu, A.M., Sidharth, M.: Approximation degree of a Kantorovich variant of Stancu operators based on Pólya–Eggenberger distribution. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. RACSAM 113, 137–156 (2019). https://doi.org/10.1007/s13398-017-0461-0

  5. Baumann, K., Heilmann, M., Raşa, I.: Further results for \(k\)th order Kantorovich modification of linking Baskakov type operators. Results Math. 69, 297–315 (2016)

    Article  MathSciNet  Google Scholar 

  6. Deo, N., Dhamija, M., Miclǎuş, D.: Stancu–Kantorovich operators based on inverse Pólya–Eggenberger distribution. Appl. Math. Comput. 273, 281–289 (2016)

    MathSciNet  MATH  Google Scholar 

  7. DeVore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, Berlin (1993)

    Book  Google Scholar 

  8. Gadjiev, A.D.: Theorems of the type of P.P. Korovkin type theorems. Math. Zametki 20(5), 781–786 (1976)

  9. Gupta, V.: Higher order Lupaş–Kantorovich operators and finite differences. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. RACSAM 115, 100 (2021). https://doi.org/10.1007/s13398-021-01034-2

  10. Gupta, V.: On difference of operators with applications to Szász type operators. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. RACSAM 113(3), 2059–2071 (2019). https://doi.org/10.1007/s13398-018-0605-x

  11. Gupta, V., Acu, A.M., Srivastava, H.M.: Difference of some positive linear approximation operators for higher-order derivatives. Symmetry 12(6), 915 (2020). https://doi.org/10.3390/sym12060915

    Article  Google Scholar 

  12. Gupta, V., Agrawal, G.: Approximation for modification of exponential type operators connected with \(x(x+1)^2\). Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. RACSAM 114, 158 (2020). https://doi.org/10.1007/s13398-020-00889-1

  13. Gupta, V., Anjali: Kantorovich variant based on inverse Pólya–Eggenberger distribution (communicated)

  14. Gupta, V., Malik, N.: Direct estimations of new generalized Baskakov–Szász operators. Publ. Math. Inst. (Beograd) 99(113), 265–279 (2016)

    Article  MathSciNet  Google Scholar 

  15. Gupta, V., Tachev, G.: Approximation with Positive Linear Operators and Linear Combinations, Series: Developments in Mathematics. Springer, Cham (2017)

  16. Ispir, N.: On modified Baskakov operators on weighted spaces. Turk. J. Math. 26(3), 355–365 (2001)

    MathSciNet  MATH  Google Scholar 

  17. Rahman, S., Mursaleen, M., Khan, A.: A Kantorovich variant of Lupaş–Stancu operators based on Pólya distribution with error estimation. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat. RACSAM 114, 75 (2020). https://doi.org/10.1007/s13398-020-00804-8

  18. Stancu, D.D.: Approximation of functions by a new class of linear polynomial operators. Rev. Roum. Math. Pures et Appl. 13, 1173–1194 (1968)

    MathSciNet  MATH  Google Scholar 

  19. Zhou, D.X.: Converse theorems for multidimensional Kantorovich operators. Anal. Math. 19, 85–100 (1993)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors are thankful to the referee(s) for valuable suggestions leading to better presentation of the paper.

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  1. Department of Mathematics, Netaji Subhas University of Technology, Sector 3 Dwarka, New Delhi, 110078, India

    Vijay Gupta &  Anjali

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  1. Vijay Gupta
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  2. Anjali
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Correspondence to Vijay Gupta.

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Gupta, V., Anjali Higher order Kantorovich operators based on inverse Pólya–Eggenberger distribution. RACSAM 116, 31 (2022). https://doi.org/10.1007/s13398-021-01176-3

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