Dergiler / Constructive Mathematical Analysis / 2018 / Volume: 1 Issue: 2

Approximation of Modified Jakimovski-Leviatan-Beta Type Operators

Mohammad Mursaleen(Aligarh Muslim University)0000-0003-4128-0427
Mohammad Nasıruzzaman(Jamia Hamdard, New Delhi)
Sayfa
—
Yayın Tarihi
2018-11-07
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also determine the order of convergence in terms of modulus of continuity, Lipschitz functions, Peetre's K-functional, second order modulus of continuity and weighted modulus of continuity.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the present paper, we define Jakimovski-Leviatan type modified operators.
📊
Temel Bulgular & Veri:We study some approximation results for these operators.
💡
Sonuç & Katkı:We also determine the order of convergence in terms of modulus of continuity, Lipschitz functions, Peetre's K-functional, second order modulus of continuity and weighted modulus of continuity.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Jakimovski-Leviatan operators · Korovkin's theorem · Modulus of continuity

Abstract

In the present paper, we define Jakimovski-Leviatan type modified operators. We study some approximation results for these operators. We also determine the order of convergence in terms of modulus of continuity, Lipschitz functions, Peetre's K-functional, second order modulus of continuity and weighted modulus of continuity.

🔖

Bu Makaleye Atıf Yap

Mursaleen, M., Nasıruzzaman, M. (2018). Approximation of Modified Jakimovski-Leviatan-Beta Type Operators. Constructive Mathematical Analysis, Volume: 1 Issue: 2. https://doi.org/10.33205/cma.453284

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (20)

  1. T. Acar, Asymptotic formulas for generalized Szász-Mirakyan operators, Appl. Math. Comput., 263 (2015) 223– 239.
  2. A. Ciupa, A class of integral Favard-Szász type operators, Stud. Univ. Babe¸s-Bolyai, Math., 40 (1995) 39–47.
  3. W. A. Al-Salam, q-Appell polynomials. Ann. Mat. Pura Appl., 4 (1967) 31–45.
  4. P. Appell, Une classe de polynômes, Ann. Sci. École Norm. Sup., 9 (1880) 119–144.
  5. A. Aral, T. Acar, Weighted approximation by new Bernstein-Chlodowsky- Gadjiev operators, Filomat, 27 (2013) 371–380.
  6. C. Atakut, I. Büyükyazici, Approximation by modified integral type Jakimovski-Leviatan operators, Filomat, 30 (2016) 29–39.
  7. İ. Büyükyazıcı, H. Tanberkan, S. Serenbay, C. Atakut, Approximation by Chlodowsky type Jakimovski-Leviatan operators, Jour. Comput. Appl. Math., 259 (2014) 153–163.
  8. J. Choi, H.M. Srivastava, q-Extensions of a multivariable and multiparameter generalization of the Gottlieb polynomials in several variables, Tokyo J. Math., 37 (2014) 111–125.
  9. A. D. Gadzhiev, A problem on the convergence of a sequence of positive linear operators on unbounded sets, and theorems that are analogous to P. P. Korovkin’s theorem. Dokl. Akad. Nauk SSSR (Russian), 218 (1974) 1001–1004.
  10. A. D. Gadzhiev, Weighted approximation of continuous functions by positive linear operators on the whole real axis, Izv. Akad. Nauk Azerbaijan. SSR Ser. Fiz.-Tehn. Mat. Nauk (Russian), 5 (1975) 41–45.
  11. P. Gupta, P. N. Agarwal, Jakimovski-Leviatan operators of Durrmeyer type involving involving Appell polynomials, Turk J. Math., 42 (2018) 1457–1470.
  12. F.H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41(15) (1910) 193–203.
  13. A. Jakimovski, D. Leviatan, Generalized Szasz operators for the approximation in the infinite interval. Mathematica (Cluj), 11 (34) (1969) 97-103.
  14. V. Kac., A. De Sole, On integral representations of q-gamma and q-beta functions, Rend. Mat. Acc. Lincei, 9 (200) 11–29.
  15. M. E. Keleshteri, N.I. Mahmudov, A study on q-Appell polynomials from determinantal point of view, Appl. Math. Comp., 260 (2015) 351–369.
  16. P. P. Korovkin, Linear Operators And Approximation Theory, Hindustan Publ. Co. Delhi, 1960.
  17. G. V. Milovanovic, M. Mursaleen., M. Nasiruzzaman, Modified Stancu type Dunkl generalization of Szász- Kantorovich operators, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 112(1) (2018) 135–151.
  18. M. Mursaleen, K.J. Ansari, M. Nasiruzzaman, Approximation by q-analogue of Jakimovski-Leviatan operators involving q-Appell polynomials, Iran. J. Sci. Technol. Trans. Sci. 41 (2017) 891–900.
  19. A. Wafi, N. Rao, D. Rai, Appproximation properties by generalized-Baskakov-Kantrovich-Stancu type operators, Appl. Math. Inform. Sci. Lett., 4 (2016) 111–118.
  20. B. Wood, Generalized Szász operators for the approximation in the complex domain, SIAM J. Appl. Math., 17 (1969) 790-801.