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ON KANTOROVICH FORM OF GENERALIZED SZASZ-TYPE OPERATORS USING CHARLIER POLYNOMIALS

Deepmala|Abdul Wafi|Nadeem Rao
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2017.03|한국수학논문집 (Korean Journal of Mathematics)|제25권 제1호|pp. 99-116|DOI http://dx.doi.org/10.11568/kjm.2017.25.1.99

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참고문헌

키워드

Lipschitz classKantorovich Sz'{a}sz operatorsCharlier polynomialsDitzian-Totik modulus of smoothnessPeetre's K-functional
주제분류수학

초록

The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

Abstract

The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

참고문헌 (27)

  1. T. Acar, "Simultaneous approximation for general-ized Srivastava-Gupta operator", Journal of Function Spaces, pp.11~ (2015)[DOI]
  2. S.N. Bernstein, "Demonstration du theoreme de Weierstrass, fondee sur le calcul des probabilites", Commun. Soc. Math. Kharkow, 2(13), pp.2~ (1913)
  3. R.A. DeVore, (1993), Springer-Verlag
  4. Z. Ditzian, "Moduli of smoothness" (1987), Springer-Verlag
  5. R.B. Gandhi, "Local and global results for modified Szász-Mirakjan operators", Mathematical Methods in the Applied Sciences, 40(7), pp.2491~2504 (2017), Wiley-Blackwell[DOI]
  6. H. Gonska, "Asymptotic behaviour of di erentiated Bernstein polyno-mials", Mat. Vesnik, 61, pp.53~60 (2009)
  7. H. Gonska, "Kantorovich operators of order k", Numer. Funct. Anal. Optimiz, 32, pp.717~738 (2011)
  8. M.E.H. Ismail, "Classical and Quantum Orthogonal Polynomials in one Variable" (2005), Cambridge University Press
  9. L.V. Kantorovich, "Sur certains developpements suivant les polyn^omes la forme de S. Bernstein, I, II, C. R", Acad URSS, 563~568 (1930)
  10. J.P. King, "Positive linear opeartors which preserves x2", Acta Math. Hungar, 99(3), pp.203~208 (2003)
  11. G.G. Lorentz, "Mathematical Expositions, No. 8, Bernstein polynomials" (1953), Univer-sity of Toronto Press
  12. V.N. Mishra, "On Simultaneous Approximation for Baskakov-Durrmeyer-Stancu type operators", Journal of Ultra Scientist of Phys-ical Sciences, 24(3), pp.567~577 (2012)
  13. Vishnu Mishra, "Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators", Journal of Inequalities and Applications, 2013(1), pp.586~ (2013), Springer Nature[DOI]
  14. V.N. Mishra, "Hypergeometric Repre-sentation for Baskakov-Durrmeyer-Stancu Type Operators", Bulletin of Mathe-matical Analysis and Applications, 5(3), pp.18~26 (2013)
  15. V.N. Mishra, "Some approximation properties of q-Baskakov-Beta-Stancu type operators", Journal of Calculus of Variations, 2013, pp.8~ (2013)[DOI]
  16. Vishnu Mishra, "Statistical approximation by Kantorovich-type discrete q-Beta operators", Advances in Difference Equations, 2013(1), pp.345~ (2013), Springer Nature[DOI]
  17. Vishnu Narayan Mishra, "On statistical approximation properties of q-Baskakov–Szász–Stancu operators", Journal of the Egyptian Mathematical Society, 24(3), pp.396~401 (2016), Elsevier BV[DOI]
  18. V.N. Mishra, "Simultaneous approximation by Szasz-Mirakjan-Durrmeyer-type operators", Bollettino dell'Unione Matematica Italiana, 8(4), pp.297~305 (2016)
  19. Vishnu Narayan Mishra, "Simultaneous approximation by Szász–Mirakjan–Stancu–Durrmeyer type operators", Periodica Mathematica Hungarica, 74(1), pp.118~127 (2017), Springer Nature[DOI]
  20. R.N. Mohapatra, "Remarks on a class of Szsz-Mirakyan type operators", East J. Approx., 15(2), pp.197~206 (2009)
  21. O. Szasz, "Generalization of S. Bernstein's polynomials to the in nite interval", J. Research Nat. Bur. Standards Sci, 45(3-4), pp.239~245 (1950)
  22. V. Totik, "Approximation by Szasz-Mirakjan-Kantorovich operators in Lp(p > 1)", Anal. Math, 9(2), pp.147~167 (1983)
  23. A. Wa, "Stancu-variant of generalized Baskakov operators", Filomat (2015)
  24. A. Wa, "Approximation properties by generalized-Baskakov-Kantorovich-Stancu type operators", Appl. Math. Inf. Sci. Lett., 4(3), pp.111~118 (2016)
  25. Abdul Wafi, "Szász-Durrmeyer Operators Based on Dunkl Analogue", Complex Analysis and Operator Theory (2017), Springer Nature[DOI]
  26. A. Wafi, "A generalization of Szasz-type operators which preserves constant and quadratic test functions", Cogent Mathematics, 3, pp.1227023~ (2016)
  27. S. Varma, "Szasz type operators involving Charlier polynomials", Math. Comput. Modeling, 56(5-6), pp.118~122 (2012)

관련 논문AI추천

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