Research Article
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Year 2020, Volume: 69 Issue: 2, 1522 - 1536, 31.12.2020
https://doi.org/10.31801/cfsuasmas.750568

Abstract

Project Number

MHR-01-23-200-428

References

  • U. Abel and V. Gupta. An estimate of the rate of convergence of a Bezier variant of the Baskakov-Kantorovich operators for bounded variation functions. Demonstr. Math., 36(1):123-136, 2003.
  • P. N. Agrawal, N. Ispir, and A. Kajla. Approximation properties of Bezier-summation-integral type operators based on Polya-Bernstein functions. Appl. Math. Comput., 259:533-539, 2015.
  • Z. Ditzian and V. Totik. Moduli of smoothness, Springer Ser. Comput. Math. Berlin, itd: Springer Verlag, 9, 1987.
  • M. Goyal and P. N. Agrawal. B´ezier variant of the Jakimovski- Leviatan-P˘alt˘anea operators based on Appell polynomials. Ann. Univ. Ferrara, 63(2):289-302, 2017.
  • S. S. Guo, G. F. Liu, and Z. J. Song. Approximation by Bernstein- Durrmeyer- Bezier operators in Lp spaces. Acta Math. Sci. Ser. A Chin. Ed, 30(6):1424-1434, 2010.
  • M. Ismail. On a generalization of Sz´asz operators. Mathematica (Cluj), 39:259-267, 1974.
  • N. Ispir and I. Yuksel. On the Bezier variant of Srivastava- Gupta operators. Appl. Math. E-Notes, 5:129-137, 2005.
  • A. Jakimovski and D. Leviatan. Generalized Szasz operators for the approximation in the infinite interval. Mathematica (Cluj), 11(34):97-103, 1969.
  • M. Mursaleen, A. AL-Abeid, and K. J. Ansari. Approximation by Jakimovski- Leviatan- Paltanea operators involving Sheffer polynomials. Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM, 113(2):1251-1265, 2019.
  • M. A. Ozarslan. Local approximation behavior of modified SMK operators. Miskolc Math. Notes, 11(1):87-99, 2010.
  • R. Paltanea. Modified Szasz- Mirakjan operators of integral form. Carpathian J. Math., pages 378-385, 2008.
  • R. S. Phillips. An inversion formula for Laplace transforms and semi-groups of linear operators. Ann. Math., pages 325-356, 1954.
  • H. M. Srivastava and V. Gupta. Rate of convergence for the Bezier variant of the Bleimann-Butzer- Hahn operators. Appl. Math. Lett., 18(8):849-857, 2005.
  • O. Szasz. Generalization of S. Bernsteins polynomials to the infinite interval. J. Res. Nat. Bur. Standards, 45:239-245, 1950.
  • D. Verma and V. Gupta. Approximation for Jakimovski- Leviatan- Paltanea operators. Ann. Univ. Ferrara, 61(2):367-380, 2015.
  • X. Zeng and A. Piriou. On the rate of convergence of two Bernstein- Bezier type operators for bounded variation functions. J. Approx. Theory, 95(3):369-387, 1998.
  • X. M. Zeng. On the rate of convergence of the generalized Szasz type operators for functions of bounded variation. J. Math. Anal. Appl., 226(2):309-325, 1998.

Approximation by Bézier variant of Jakimovski-Leviatan-Păltănea operators involving Sheffer polynomials

Year 2020, Volume: 69 Issue: 2, 1522 - 1536, 31.12.2020
https://doi.org/10.31801/cfsuasmas.750568

Abstract

In the present paper, the Bezier variant of Jakimovski-Leviatan-Peltenea operators involving Sheffer polynomials is introduced and the degree of approximation by these operators is investigated with the aid of Ditzian-Totik modulus of smoothness, Lipschitz type space and for functions with derivatives of bounded variations.

Supporting Institution

Indian Institute of Technology Roorkee

Project Number

MHR-01-23-200-428

Thanks

The second author is extremely grateful to the Ministry of Human Resource Development of India to carry out his research work.

References

  • U. Abel and V. Gupta. An estimate of the rate of convergence of a Bezier variant of the Baskakov-Kantorovich operators for bounded variation functions. Demonstr. Math., 36(1):123-136, 2003.
  • P. N. Agrawal, N. Ispir, and A. Kajla. Approximation properties of Bezier-summation-integral type operators based on Polya-Bernstein functions. Appl. Math. Comput., 259:533-539, 2015.
  • Z. Ditzian and V. Totik. Moduli of smoothness, Springer Ser. Comput. Math. Berlin, itd: Springer Verlag, 9, 1987.
  • M. Goyal and P. N. Agrawal. B´ezier variant of the Jakimovski- Leviatan-P˘alt˘anea operators based on Appell polynomials. Ann. Univ. Ferrara, 63(2):289-302, 2017.
  • S. S. Guo, G. F. Liu, and Z. J. Song. Approximation by Bernstein- Durrmeyer- Bezier operators in Lp spaces. Acta Math. Sci. Ser. A Chin. Ed, 30(6):1424-1434, 2010.
  • M. Ismail. On a generalization of Sz´asz operators. Mathematica (Cluj), 39:259-267, 1974.
  • N. Ispir and I. Yuksel. On the Bezier variant of Srivastava- Gupta operators. Appl. Math. E-Notes, 5:129-137, 2005.
  • A. Jakimovski and D. Leviatan. Generalized Szasz operators for the approximation in the infinite interval. Mathematica (Cluj), 11(34):97-103, 1969.
  • M. Mursaleen, A. AL-Abeid, and K. J. Ansari. Approximation by Jakimovski- Leviatan- Paltanea operators involving Sheffer polynomials. Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM, 113(2):1251-1265, 2019.
  • M. A. Ozarslan. Local approximation behavior of modified SMK operators. Miskolc Math. Notes, 11(1):87-99, 2010.
  • R. Paltanea. Modified Szasz- Mirakjan operators of integral form. Carpathian J. Math., pages 378-385, 2008.
  • R. S. Phillips. An inversion formula for Laplace transforms and semi-groups of linear operators. Ann. Math., pages 325-356, 1954.
  • H. M. Srivastava and V. Gupta. Rate of convergence for the Bezier variant of the Bleimann-Butzer- Hahn operators. Appl. Math. Lett., 18(8):849-857, 2005.
  • O. Szasz. Generalization of S. Bernsteins polynomials to the infinite interval. J. Res. Nat. Bur. Standards, 45:239-245, 1950.
  • D. Verma and V. Gupta. Approximation for Jakimovski- Leviatan- Paltanea operators. Ann. Univ. Ferrara, 61(2):367-380, 2015.
  • X. Zeng and A. Piriou. On the rate of convergence of two Bernstein- Bezier type operators for bounded variation functions. J. Approx. Theory, 95(3):369-387, 1998.
  • X. M. Zeng. On the rate of convergence of the generalized Szasz type operators for functions of bounded variation. J. Math. Anal. Appl., 226(2):309-325, 1998.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

P. Agrawal This is me 0000-0003-3029-6896

Ajay Kumar 0000-0002-0739-9232

Project Number MHR-01-23-200-428
Publication Date December 31, 2020
Submission Date June 10, 2020
Acceptance Date November 11, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Agrawal, P., & Kumar, A. (2020). Approximation by Bézier variant of Jakimovski-Leviatan-Păltănea operators involving Sheffer polynomials. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1522-1536. https://doi.org/10.31801/cfsuasmas.750568
AMA Agrawal P, Kumar A. Approximation by Bézier variant of Jakimovski-Leviatan-Păltănea operators involving Sheffer polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1522-1536. doi:10.31801/cfsuasmas.750568
Chicago Agrawal, P., and Ajay Kumar. “Approximation by Bézier Variant of Jakimovski-Leviatan-Păltănea Operators Involving Sheffer Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1522-36. https://doi.org/10.31801/cfsuasmas.750568.
EndNote Agrawal P, Kumar A (December 1, 2020) Approximation by Bézier variant of Jakimovski-Leviatan-Păltănea operators involving Sheffer polynomials. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1522–1536.
IEEE P. Agrawal and A. Kumar, “Approximation by Bézier variant of Jakimovski-Leviatan-Păltănea operators involving Sheffer polynomials”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1522–1536, 2020, doi: 10.31801/cfsuasmas.750568.
ISNAD Agrawal, P. - Kumar, Ajay. “Approximation by Bézier Variant of Jakimovski-Leviatan-Păltănea Operators Involving Sheffer Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1522-1536. https://doi.org/10.31801/cfsuasmas.750568.
JAMA Agrawal P, Kumar A. Approximation by Bézier variant of Jakimovski-Leviatan-Păltănea operators involving Sheffer polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1522–1536.
MLA Agrawal, P. and Ajay Kumar. “Approximation by Bézier Variant of Jakimovski-Leviatan-Păltănea Operators Involving Sheffer Polynomials”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1522-36, doi:10.31801/cfsuasmas.750568.
Vancouver Agrawal P, Kumar A. Approximation by Bézier variant of Jakimovski-Leviatan-Păltănea operators involving Sheffer polynomials. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1522-36.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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