DOI QR코드

DOI QR Code

APPROXIMATION BY GENUINE LUPAŞ-BETA-STANCU OPERATORS

  • KUMAR, ALOK (Department of Computer Science, Dev Sanskriti Vishwavidyalaya) ;
  • VANDANA, VANDANA (Department of Management Studies, Indian Institute of Technology)
  • 투고 : 2017.10.09
  • 심사 : 2017.12.16
  • 발행 : 2018.01.30

초록

In this paper, we introduce a Stancu type generalization of genuine LupaŞ-Beta operators of integral type. We establish some moment estimates and the direct results in terms of classical modulus of continuity, Voronovskaja-type asymptotic theorem, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Lastly, we propose a king type modification of these operators to obtain better estimates.

키워드

참고문헌

  1. R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer, Berlin (1993).
  2. T. Acar, L.N. Mishra and V.N. Mishra, Simultaneous Approximation for Generalized Srivastava-Gupta Operators, Journal of Function Spaces 2015, Article ID 936308, 11 pages.
  3. A.D. Gadjiev, Theorems of the type of P. P. korovkin's theorems, Matematicheskie Zametki 20 (1976), 781-786.
  4. A.D. Gadjiev, R.O. Efendiyev and E. Ibikli, On Korovkin type theorem in the space of locally integrable functions, Czechoslovak Math. J. 1(128) (2003), 45-53.
  5. A.R. Gairola, Deepmala and L.N. Mishra, On the q-derivatives of a certain linear positive operators, Iranian Journal of Science and Technology, Transactions A: Science, (2017), DOI 10.1007/s40995-017-0227-8.
  6. A.R. Gairola, Deepmala and L.N. Mishra, Rate of Approximation by Finite Iterates of q-Durrmeyer Operators, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (April-June 2016) 86:229-234 (2016). doi: 10.1007/s40010-016-0267-z
  7. V. Gupta, Th.M. Rassias and E. Pandey, On genuine Lupas-Beta operators and modulus of continuity, Int. J. Nonlinear Anal. Appl. 8 (2017), 23-32.
  8. V. Gupta, Th.M. Rassias and R. Yadav, Approximation by Lupas-Beta integral operators, Appl. Math. Comput. 236 (2014), 19-26.
  9. V. Gupta and R. Yadav, On approximation of certain integral operators, Acta Math. Vietnamica 39 (2014), 193-203. https://doi.org/10.1007/s40306-014-0057-0
  10. N.K. Govil, V. Gupta and D. Soybas, Certain new classes of Durrmeyer type operators, Appl. Math. Comput. 225 (2013), 195-203.
  11. V. Gupta, Th.M. Rassias and J. Sinha, A survey on Durrmeyer operators, Springer International Publishing Switzerland, (2016), 299-312, Contributions in Mathematics and Engineering P.M. Pardalos, T.M. Rassias (eds.).
  12. G.C. Jain, Approximation of functions by a new class of linear operators, J. Aust. Math. Soc. 13 (1972), 271-276. https://doi.org/10.1017/S1446788700013689
  13. A. Kumar, Voronovskaja type asymptotic approximation by general Gamma type operators, Int. J. of Mathematics and its Applications 3 (2015), 71-78.
  14. A. Kumar, Approximation by Stancu type generalized Srivastava-Gupta operators based on certain parameter, Khayyam J. Math. 3, no. 2 (2017), pp. 147-159. DOI:10.22034/kjm.2017.49477
  15. A. Kumar, General Gamma type operators in $L^p$ spaces, Palestine Journal of Mathematics 7 (2018), 73-79.
  16. A. Kumar and D. K. Vishwakarma, Global approximation theorems for general Gamma type operators, Int. J. of Adv. in Appl. Math. and Mech. 3(2) (2015), 77-83.
  17. A. Kumar and L.N. Mishra, Approximation by modified Jain-Baskakov-Stancu operators, Tbilisi Mathematical Journal 10 (2017), pp. 185-199.
  18. A. Kumar, V.N. Mishra and Dipti Tapiawala, Stancu type generalization of modified Srivastava-Gupta operators, Eur. J. Pure Appl. Math 10, (2017), 890-907.
  19. A. Kumar, Artee and D.K. Vishwakarma, Approximation properties of general gamma type operators in polynomial weighted space, Int. J. Adv. Appl. Math. and Mech. 4 (2017), pp. 7-13.
  20. J.P. King, Positive linear operators which preserve $x^2$, Acta Math. Hungar. 99 (2003), 203-208. https://doi.org/10.1023/A:1024571126455
  21. B. Lenze, On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math. 50 (1988), 53-63.
  22. N.I. Mahmudov and V. Gupta, On certain q-analogue of Szasz Kantorovich operators, J. Appl. Math. Comput. 37 (2011), 407-419. https://doi.org/10.1007/s12190-010-0441-4
  23. V.N. Mishra, P. Sharma and M. Birou, Approximation by Modified Jain-Baskakov Operators, arXiv:1508.05309v2 [math.FA] 9 Sep 2015.
  24. V.N. Mishra and P. Sharma, On approximation properties of Baskakov-Schurer-Szasz operators, arXiv:1508.05292v1 [math.FA] 21 Aug 2015.
  25. V.N. Mishra, H.H. Khan, K. Khatri and L.N. Mishra, Hypergeometric Representation for Baskakov-Durrmeyer-Stancu Type Operators, Bulletin of Mathematical Analysis and Applications 5 Issue 3 (2013), Pages 18-26.
  26. V.N. Mishra, K. Khatri and L.N. Mishra, On Simultaneous Approximation for Baskakov-Durrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences 24, 3(A) (2012), pp. 567-577.
  27. V.N. Mishra, K. Khatri, L.N. Mishra and Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications (2013), 2013:586. doi:10.1186/1029-242X-2013-586.
  28. V.N. Mishra, K. Khatri and L.N. Mishra, Some approximation properties of q-BaskakovBeta-Stancu type operators, Journal of Calculus of Variations 2013, Article ID 814824, 8 pages.
  29. V.N. Mishra, Rajiv B. Gandhi and Ram N. Mohapatraa, Summation-Integral type modification of Szasz-Mirakjan-Stancu operators, J. Numer. Anal. Approx. Theory 45(1) (2016), pp. 27-36.
  30. V.N. Mishra, K. Khatri, L.N. Mishra and Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, J. Inequal. Appl. 586 (2013), 1-11.
  31. M.A. Ozarslan and H. Aktuglu, Local approximation for certain King type operators, Filomat 27 (2013), 173-181. https://doi.org/10.2298/FIL1301173O
  32. E. Pandey and R.K. Mishra, Convergence estimates in simultaneous approximation by certain Srivastava-Gupta type operators, Adv. Studies Contemporary Math. 26 (2016), 467-480.
  33. D.D. Stancu, Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures Appl. 13 (1968), 1173-1194.
  34. O. Szasz, Generalization of S. Bernstein polynomials to the infinite interval, J. Res. Natl. Bur. Stand. 45 (1950), 239-245. https://doi.org/10.6028/jres.045.024