Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers

References

[1] Acar, T.: (p, q)-generalization of Szász-Mirakyan operators, Math. Methods Appl. Sci. 39(10) (2016), 2685–2695.10.1002/mma.3721Search in Google Scholar

[2] Acar, T.—Aral, A.—Mohiuddine, S. A.: Approximation by bivariate (p, q)-Bernstein-Kantorovich operators, Iran. J. Sci. Technol. Trans. A Sci. (2016), 10.1007/s40995-016-0045-4.Search in Google Scholar

[3] Acar, T.—Aral, A.—Mohiuddine, S. A.: On Kantorovich modifications of (p, q)-Baskakov operators, J. Inequal. Appl. (2016), 2016: 98.10.1186/s13660-016-1045-9Search in Google Scholar

[4] Acar, T.—Agrawal, P. N.—Kumar, S.: On a modification of (p, q)-Szasz-Mirakyan operators, Comp. Anal. Oper. Theo. 12 (2018), 155–167.10.1007/s11785-016-0613-9Search in Google Scholar

[5] Aral, A.—Gupta, V.: Generalized q-Baskakov operators, Math. Slovaca 61 (2011), 619–634.10.2478/s12175-011-0032-3Search in Google Scholar

[6] Aral, A.—Gupta, V.: Applications of (p, q)-gamma function to Szasz-Durrmeyer operators, Publications de ľInstitut Mathematique, In Press.Search in Google Scholar

[7] Aral, A.—Gupta, V.: (p, q)-Type beta functions of second kind, Advances in Operator Theory 1(1) (2016), 134–146.Search in Google Scholar

[8] Burban, I.: Two-parameter deformation of the oscillator albegra and (p, q) analog of two dimensional conformal field theory, J. Nonlinear Math. Phys. 2(3–4) (1995), 384–391.10.2991/jnmp.1995.2.3-4.18Search in Google Scholar

[9] Burban, I.—Klimyk, A. U.: P, Q differentiation, P, Q integration and P, Q hypergeometric functions related to quantum groups, Integral Transforms Spec. Funct. 2(1) (1994), 15–36.10.1080/10652469408819035Search in Google Scholar

[10] Devore, R. A.—Lorentz G. G.: Constructive Approximation, Springer, Berlin, 1993.10.1007/978-3-662-02888-9Search in Google Scholar

[11] Hounkonnou, M. N.—Desire, J.—Kyemba, B.: 𝓡(p, q)-calculus: differentiation and integration, SUT J. Math. 49(2) (2013), 145–167.10.55937/sut/1394548362Search in Google Scholar

[12] Ibikli, E.—Gadjieva, E. A.: The order of approximation of some unbounded function by the sequences of positive linear operators, Turk. J. Math. 19(3) (1995), 331–337.Search in Google Scholar

[13] Jagannathan, R.—Rao, K. S.: Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series. In: Proceedings of the International Conference on Number Theory and Mathematical Physics, 20–21 December 2005.Search in Google Scholar

[14] King, J. P.: Positive linear operators which preserves x², Acta. Math. Hungar. 99 (2003), 203–208.10.1023/A:1024571126455Search in Google Scholar

[15] Lenze, B.: On Lipschitz type maximal functions and their smoothness spaces, Indag. Math. 50 (1988), 53–63.10.1016/1385-7258(88)90007-8Search in Google Scholar

[16] Mursaleen, M.—Ansari, K. J.—Khan, A.: On (p, q)-analogue of Bernstein operators, Appl. Math. Comput. 266 (2015), 874–882.10.1016/j.amc.2015.04.090Search in Google Scholar

[17] Mursaleen, M.—Ansari, K. J.—Khan, A.: Some approximation results by (p, q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput. 264 (2015), 392–402 [Corrigendum: Appl. Math. Comput. 269 (2015), 744–746].10.1016/j.amc.2015.03.135Search in Google Scholar

[18] Mursaleen, M.—Nasiruzzaman, Md.—Khan, A.—Ansari, K. J.: Some approximation results on Bleimann-Butzer-Hahn operators defined by (p, q)-integers, Filomat 30(3) (2016), 639–648.10.2298/FIL1603639MSearch in Google Scholar

[19] Mursaleen, M.—Nasiruzzaman, Md.—Nurgali, A.: Some approximation results on Bernstein-Schurer operators defined by (p, q)-integers, J. Ineq. Appl. 2015 (2015), 249.10.1186/s13660-015-0767-4Search in Google Scholar

[20] Sadjang, P. N.: On the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulas, arXiv:1309.3934 [math.QA].Search in Google Scholar

[21] Sahai, V.—Yadav, S.: Representations of two parameter quantum algebras and p, q-special functions, J. Math. Anal. Appl. 335 (2007), 268–279.10.1016/j.jmaa.2007.01.072Search in Google Scholar