Skip to main content
SpringerLink
Log in

Approximation by Integral form of Jain and Pethe Operators

  • Research Article
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we consider the integral form of Jain and Pethe operators associated with the Baskakov operators and study some basic properties. We estimate the rate of convergence, Voronovskaja-type asymptotic estimate formula and weighted approximation of these operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Jain GC, Pethe S (1977) On the generalizations of Bernstein and Szász–Mirakyan operators. Nanta Math 10:185–193

    MathSciNet  MATH  Google Scholar 

  2. Dhamija M, Pratap R, Deo N (2018) Approximation by Kantorovich form of modified Szász–Mirakyan Operators. Appl Math Comput 317:109–120

    MathSciNet  MATH  Google Scholar 

  3. Abel U, Ivan M (2007) On a generalization of an approximation operator defined by A Lupas. Gen Math 15(1):21–34

    MathSciNet  MATH  Google Scholar 

  4. Stancu DD (1980) A study of the remainder in an approximation formula using a Favard–Szász type operator. Stud Univ Babeş-Bolyai Math XXV:70–76

    MATH  Google Scholar 

  5. Mastroianni G (1980/1981) Una generalizzazione dell‘operatore di Mirakyan. Rend Accad Sci Fis Mat Napoli Serie IV, XLVIII:237–252

  6. Della Vecchia B, Kocic LM (1988) On the degeneracy property of some linear positive operators. Calcolo 25(4):363–377

    Article  MathSciNet  Google Scholar 

  7. Finta Z (2001) Pointwise approximation by generalized Szász–Mirakjan operators. Stud Univ Babeş-Bolyai Math 46(4):61–67

    MathSciNet  MATH  Google Scholar 

  8. Finta Z (2002) On approximation properties of Stancu’s operators. Studia Univ Babeş–Bolyai Math XLVI I(4):47–55

    MathSciNet  MATH  Google Scholar 

  9. Baskakov VA (1957) A sequence of linear positive operators in the space of continuous functions. Dokl Acad Nauk SSSR 113:249–251

    MathSciNet  MATH  Google Scholar 

  10. Sahai A, Prasad G (1985) On Simultaneous approximation by modified Lupas operators. J Approx Theory 45:122–128

    Article  MathSciNet  Google Scholar 

  11. Durrmeyer JL (1967) Une formule d’inversion de la transformée de Laplace-applications à la théorie des moments, Thése de 3e cycle, Faculté des Sciences de l’ Université de Paris

  12. Abel U, Gupta V, Mahapatra RN (2008) Local approximation by a variant of Bernstein–Durrmeyer operators. Nonlinear Anal Theory Methods Appl 68(11):3372–3381

    Article  MathSciNet  Google Scholar 

  13. Agrawal RP, Gupta V (2012) On q-analogue of a complex summation-integral type operators in compact disks. J Inequal Appl 1:111

    Article  MathSciNet  Google Scholar 

  14. Dhamija M, Deo N (2016) Jain–Durrmeyer operators associated with the inverse Pólya–Eggenberger distribution. Appl Math Comput 286:15–22

    MathSciNet  MATH  Google Scholar 

  15. Gupta V (2003) Rate of approximation by a new sequence of linear positive operators. Comput Math Appl 45(12):1895–1904

    Article  MathSciNet  Google Scholar 

  16. Gupta V (2019) A note on the general family of operators preserving linear functions. RACSAM 113:3717–3725

    Article  MathSciNet  Google Scholar 

  17. Gupta V, Deo N, Zeng XM (2013) Simultaneous approximation for Szász–Mirakian–Stancu–Durrmeyer operators. Anal Theory Appl 29(1):86–96

    Article  MathSciNet  Google Scholar 

  18. Gupta V, Maheshwari P (1988) Bezier variant of a new Durrmeyer type operators. Bull Soc Math Belg Ser B40(1):61–71

    Google Scholar 

  19. Gupta V, Noor MA (2003) Convergence of derivatives for certain mixed Szász-Beta operators. Riv Mat Univ Parma 7(2):9–21

    MATH  Google Scholar 

  20. DeVore RA, Lorentz GG (1993) Constructive approximation. Springer, Berlin

    Book  Google Scholar 

  21. Korovkin PP (1953) Convergence of linear positive operators in the spaces of continuous functions (in Russian). Doklady Akad Nauk SSSR(N N) 90:961–964

  22. Altomare F, Campiti M (1994) Korovkin-type approximation theory and its application, de Gruyter studies in mathematics, vol 17, Walter de Gruyter & Co, Berlin

  23. Szász O (1950) Generalizations of S Bernstein’s polynomial to the infinite interval. J Res Nat Bur Stand 45:239–245

    Article  MathSciNet  Google Scholar 

  24. Zhuk VV (1989) Functions of the \(Lip_{1}\) class and S N Bernstein’s polynomials (in Russian). Vestnik Leningr Univ Mat Mekh Astronom 1:25–30

    Google Scholar 

  25. Ditzian Z, Totik V (1987) Moduli of smoothness. In: Springer series in computational mathematics, vol 9, Springer, New York

  26. İbekli E, Gadjieva EA (1995) The order of approximation of some unbounded functions by the sequences of positive linear operators. Turk J Math 19(3):331–337

    MathSciNet  MATH  Google Scholar 

  27. Yüksel I, Ispir N (2006) Weighted approximation by a certain family of summation integral-type operators. Comput Math Appl 52:1463–1470

    Article  MathSciNet  Google Scholar 

Download references

Funding

The funding was provided by Delhi Technological University.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, Delhi, 110042, India

    Naokant Deo & Ram Pratap

Authors
  1. Naokant Deo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ram Pratap
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ram Pratap.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deo, N., Pratap, R. Approximation by Integral form of Jain and Pethe Operators. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 92, 31–38 (2022). https://doi.org/10.1007/s40010-020-00691-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-020-00691-z

Keywords

Mathematics Subject Classification

Search

Navigation