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On Baskakov–Szász–Mirakyan-type operators preserving exponential type functions

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Abstract

The current article deals with the study of Baskakov–Szász–Mirakyan operators which reproduces constant and exponential functions. We discuss a uniform estimate and establish a quantitative result for the modified operators.

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References

  1. Acar, T., Aral, A., Gonska, H.: On Szász–Mirakyan operators preserving \(e^{2ax}\), a>0. Mediterr. J. Math. 14(1), 6 (2017)

    Article  MATH  Google Scholar 

  2. Acar, T.: Asymptotic formulas for generalized Szász–Mirakyan operators. Appl. Math. Comput. 263, 233–239 (2015)

    MathSciNet  Google Scholar 

  3. Acar, T., Ulusoy, G.: Approximation by modified Szász–Durrmeyer operators. Period. Math. Hung. 72(1), 64–75 (2016)

    Article  MATH  Google Scholar 

  4. Acar, T., Aral, A., Rasa, I.: The new forms of Voronovskayas theorem in weighted spaces. Positivity 20(1), 25–40 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Acar, T.: Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators. Georgian Math. J. 23(4), 459–468 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Acar, T., Aral, A., Cárdenas-Morales, D., Garrancho, P.: Szász–Mirakyan type operators which fix exponentials. Results Math. 72(3), 1393–1400 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. Agrawal, P.N., Mohammad, A.J.: Linear combination of a new sequence of linear positive operators. Rev. Union Mat. Argent. 44(1), 33–41 (2003)

    MathSciNet  MATH  Google Scholar 

  8. Boyanov, B.D., Veselinov, V.M.: A note on the approximation of functions in an infinite interval by linear positive operators. Bull. Math. Soc. Sci. Math. Roum. 14(62), 9–13 (1970)

    MathSciNet  MATH  Google Scholar 

  9. Gupta, V.: Approximation by Generalizations of Hybrid Baskakov Type Operators Preserving Exponential Functions, Mathematical Analysis and Applications: Selected Topics. Wiley, Hoboken (2017)

    Google Scholar 

  10. Gupta, V., Agarwal, R.P.: Convergence Estimates in Approximation Theory. Springer, Berlin (2014)

    Book  MATH  Google Scholar 

  11. Gupta, V., Aral, A.: A note on Szász–Mirakyan–Kantorovich type operators preserving \(e^{-x}\). Positivity (2017). https://doi.org/10.1007/s11117-017-0518-5

  12. Gupta, V., Tachev, G.: On approximation properties of Phillips operators preserving exponential functions. Mediterr. J. Math. 14(4), 177 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Holhoş, A.: The rate of approximation of functions in an infinite interval by positive linear operators. Stud. Univ. Babe-Bolyai Math. 2, 133–142 (2010)

    MathSciNet  MATH  Google Scholar 

  14. Ulusoy, G., Acar, T.: q-Voronovskaya type theorems for q-Baskakov operators. Math. Methods Appl. Sci. 39(12), 3391–3401 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The research work of the second author is supported from Lucian Blaga University of Sibiu research Grants LBUS-IRG-2017-03.

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Authors and Affiliations

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

    Vijay Gupta

  2. Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012, Sibiu, Romania

    Ana Maria Acu

Authors
  1. Vijay Gupta
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  2. Ana Maria Acu
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Correspondence to Ana Maria Acu.

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Gupta, V., Acu, A.M. On Baskakov–Szász–Mirakyan-type operators preserving exponential type functions. Positivity 22, 919–929 (2018). https://doi.org/10.1007/s11117-018-0553-x

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  • DOI: https://doi.org/10.1007/s11117-018-0553-x

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