Home Some approximation results for operators of Szász-Mirakjan-Durrmeyer type
Article
Licensed
Unlicensed Requires Authentication

Some approximation results for operators of Szász-Mirakjan-Durrmeyer type

  • Grażyna Krech EMAIL logo
Published/Copyright: November 3, 2016
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

Abstract

In this paper certain integral operators of Szász-Mirakjan-Durrmeyer type are presented. Some approximation results and a Voronovskaya type theorem are obtained for these operators.

MSC 2010: primary 41A25; Secondary 41A36
Keywords: positive linear operators; Szász-Mirakjan-Durrmeyer operators; degree of approximation; Voronovskaya type theorem

(Communicated by Gregor Dolinar)

Acknowledgements

The author is extremely thankful to the referee for making valuable suggestions, leading to the better presentation of the paper.

References

1 Duman, O.—Özarslan, M. A.: Global approximation results for modified Szász-Mirakjan operators, Taiwanese J. Math. 15 (2011), 75—86.10.11650/twjm/1500406162Search in Google Scholar

2 Durrmeyer, J. L.: Une formule d'inversion de la transformée de Laplace: Applications `a la théorie des moments. Th`ese de 3`eme cycle, Faculté des Sciences Univ. Paris, 1967.Search in Google Scholar

3 Heilmann, M.: Direct and converse results for operators of Baskakov-Durrmeyer type, J. Approx. Theory Appl. 5 (1989), 105—127.10.1007/BF02836120Search in Google Scholar

4 Herzog, M.: Approximation theorems for Szász-Mirakyan-Mirakyan operators in polynomial weight spaces, Matematiche (Catania) 54 (1999), 77—90.Search in Google Scholar

5 Herzog, M.: Approximation of functions from exponential weight spaces by operators of Szász-Mirakyan type, Comment. Math. XLIII (2003), 77—94.Search in Google Scholar

6 Ozarslan, M. A.: q-Szász Schurer operators, Miskolc Math. Notes 12 (2011), 225—235.10.18514/MMN.2011.257Search in Google Scholar

7 Ozarslan, M. A.—Duman, O.: Global approximation properties of modified SMK operators, Filomat 24 (2010), 47—61.10.2298/FIL1001047OSearch in Google Scholar

8 Rempulska, L.—Graczyk, S.: On generalized Szász-Mirakyan operators of functions of two variables, Math. Slovaca 62 (2012), 87—98.10.2478/s12175-011-0074-6Search in Google Scholar

9 Rempulska, L.—Graczyk, S.: On certain class of Szász-Mirakyan operators in exponential weight spaces, Int. J. Pure Appl. Math. 60 (2010), 259—267.Search in Google Scholar

10 Mazhar, S. M.—Totik, V.: Approximation by modified Szász operators, Acta Sci. Math. (Szeged) 49 (1985), 257—269.Search in Google Scholar

11 Sahai, A.—Prasad, G.: On simultaneous approximation by modified Lupas operators, J. Approx. Theory 45 (1985), 122—128.10.1016/0021-9045(85)90039-5Search in Google Scholar

12 Watson, G. N.: Theory of Bessel Functions, Cambridge Univ. Press, Cambridge, 1966.Search in Google Scholar

Received: 2013-6-18
Accepted: 2014-3-22
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Research Article
  2. Effect algebras with a full set of states
  3. Research Article
  4. An approach to orthomodular lattices via lattices with an antitone involution
  5. Research Article
  6. On properties of the free BCI-algebra with one generator
  7. Research Article
  8. The generalized order-k Narayana's cows numbers
  9. Research Article
  10. The irrationality of infinite series of a special kind
  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
  16. On a subclass of analytic functions involving Sălăgean integral operator
  17. Research Article
  18. Uniqueness of meromorphic functions sharing a value or small function
  19. Research Article
  20. A new inclusion for Bavrin's families of holomorphic functions in n-circular domains
  21. Research Article
  22. Oscillation of nonlinear fourth order mixed neutral differential equations
  23. Research Article
  24. Oscillation results for third order nonlinear mixed neutral differential equations
  25. Research Article
  26. Homoclinic solutions for second order Hamiltonian systems with general potentials
  27. Research Article
  28. A class of fractional impulsive functional differential equations with nonlocal conditions
  29. Research Article
  30. The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions
  31. Research Article
  32. On the well posed solutions for nonlinear second order neutral difference equations
  33. Research Article
  34. Some approximation results for operators of Szász-Mirakjan-Durrmeyer type
  35. Research Article
  36. On the geometry of conditional expectations treated as projections on the L2-space
  37. Research Article
  38. Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators
  39. Research Article
  40. A necessary condition for the Smith equivalence of G-modules and its sufficiency
  41. Research Article
  42. On the internal approach to differential equations. 1. The involutiveness and standard basis
  43. Research Article
  44. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three
https://doi.org/10.1515/ms-2015-0194
Keywords for this article
positive linear operators; Szász-Mirakjan-Durrmeyer operators; degree of approximation; Voronovskaya type theorem

Articles in the same Issue

  1. Research Article
  2. Effect algebras with a full set of states
  3. Research Article
  4. An approach to orthomodular lattices via lattices with an antitone involution
  5. Research Article
  6. On properties of the free BCI-algebra with one generator
  7. Research Article
  8. The generalized order-k Narayana's cows numbers
  9. Research Article
  10. The irrationality of infinite series of a special kind
  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
  16. On a subclass of analytic functions involving Sălăgean integral operator
  17. Research Article
  18. Uniqueness of meromorphic functions sharing a value or small function
  19. Research Article
  20. A new inclusion for Bavrin's families of holomorphic functions in n-circular domains
  21. Research Article
  22. Oscillation of nonlinear fourth order mixed neutral differential equations
  23. Research Article
  24. Oscillation results for third order nonlinear mixed neutral differential equations
  25. Research Article
  26. Homoclinic solutions for second order Hamiltonian systems with general potentials
  27. Research Article
  28. A class of fractional impulsive functional differential equations with nonlocal conditions
  29. Research Article
  30. The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions
  31. Research Article
  32. On the well posed solutions for nonlinear second order neutral difference equations
  33. Research Article
  34. Some approximation results for operators of Szász-Mirakjan-Durrmeyer type
  35. Research Article
  36. On the geometry of conditional expectations treated as projections on the L2-space
  37. Research Article
  38. Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators
  39. Research Article
  40. A necessary condition for the Smith equivalence of G-modules and its sufficiency
  41. Research Article
  42. On the internal approach to differential equations. 1. The involutiveness and standard basis
  43. Research Article
  44. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 22.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0194/html?lang=en
Scroll to top button