On Chlodowsky Variant of (p,q) Kantorovich-Stancu-Schurer Operators

Main Article Content

Vishnu Narayan Mishra, Shikha Pandey

Abstract

In the present paper, we introduce the Chlodowsky variant of (p,q) Kantorovich-Stancu-Schurer operators on the unbounded domain which is a generalization of (p,q) Bernstein-Stancu-Kantorovich operators. We have also derived its Korovkin type approximation properties and rate of convergence.

Article Details

References

  1. T. Acar, (p,q)-Generalization of Szász-Mirakyan operators, Math. Meth. Appl. Sci., 2015 (2015), DOI: 10.1002/mma.3721.
  2. I. M. Burban, A. U. Klimyk, (p,q)-differentiation, (p,q)-integration, and (p,q)-hypergeometric functions related to quantum groups, Integral Transforms and Special Functions, 2 (1994), 15-36.
  3. N. L. Braha, H. M. Srivastava and S. A. Mohiuddine, A Korovkin's type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean, Appl. Math. Comput. 228 (2014), 162-169.
  4. R.A. Devore, G.G. Lorentz, Constructive Approximation, Springer, Berlin,1993.
  5. A. D. Gadjiev, The convergence problem for a sequence of positive linear operators on unbounded sets and theorems analogues to that of P.P. Korovkin, Dokl. Akad. Nauk SSSR, 218 (5), 1001-1004. English translation in Sov. Math. Dokl., 15 (1974), 1433-1436.
  6. A.R. Gairola, Deepmala, L.N. Mishra, Rate of Approximation by Finite Iterates of q-Durrmeyer Operators, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2016 (2016), doi: 10.1007/s40010-016-0267-z.
  7. E. Ibikli, Approximation by Bernstein-Chlodowsky polynomials, Hacettepe Journal of Mathematics and Statistics, 32 (2003), 1-5.
  8. V.N. Mishra, K. Khatri, L.N. Mishra, Deepmala; Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications, 2013 (2013), Article ID 586.
  9. V.N. Mishra, K. Khatri, L.N. Mishra; On Simultaneous Approximation for Baskakov-Durrmeyer-Stancu type operators, Journal of Ultra Scientist of Physical Sciences, 24 (2012), 567-577.
  10. V.N. Mishra, K. Khatri, L.N. Mishra; Statistical approximation by Kantorovich type Discrete q-Beta operators, Advances in Difference Equations 2013 (2013), Article ID 345.
  11. V.N. Mishra, S. Pandey, On (p,q) Baskakov-Durrmeyer-Stancu Operators, arXiv:1602.06719 [math.CA]
  12. V.N. Mishra, S. Pandey, (p,q)-Szász-Mirakyan-Baskakov-Stancu type Operators, arXiv:1602.06312 [math.CA].
  13. M. Mursaleen, K.J. Ansari, A. Khan, On (p,q)-analogue of Bernstein operators, Appl. Math. Comput., 266 (2015), 874-882.
  14. M. Mursaleen, K.J. Ansari, A. Khan, Some approximation results by (p,q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput., 264 (2015), 392-402.
  15. M. Mursaleen, F. Khan, Approximation by Kantorovich type (p,q)-Bernstein Schurer operators, arXiv:1506.02492 [math.CA].
  16. M. Mursaleen, Md. Nasiruzzaman, A. Khan, K.J. Ansari, Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers, arXiv:1505.00392, [math.CA].
  17. M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput. 219 (2013), 6911-6818.
  18. H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inform. Sci. 5 (2011), 390-444.
  19. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
  20. T. Vedi and Mehmet AliÖzarslan, Chlodowsky-type q-Bernstein-Stancu-Kantorovich operators, J. Inequal. Appl., 2015 (2015), Article ID 91.
  21. A. Wafi, N. Rao, Deepmala, Approximation properties by generalized-Baskakov-Kantorovich-Stancu type operators, Appl. Math. Inf. Sci. Lett., 4 (2016), 1-8.