Gama Tipi Operatörün (p, q)-tamsayı İkililerine Dayalı Yaklaşım Özellikleri

Literatürde; q ve (p,q)-hesabı üzerindeki kapsamlı çalışma q ve (p,q)-tamsayı ikililerini içeren birçok operatörün farklı genellemelerinin tanımlanmasına büyük ölçüde katkıda bulunmuştur. Size sunacağımız bu çalışmada (p,q)-tamsayı ikililerine göre gama tipi operatörü tanımlayarak süreklilik modül açısından asimtotik formül ve hata tahmini içeren bazı doğrudan sonuçlar elde edeceğiz. Ayrıca, bu operatörlerin ağırlıklı bir uzayda yakınsaklığını araştırarak ve yakınsaklık oranını tahmin ediyoruz.

On Approximation Properties of Gamma Type Operator Based on (p,q)-İnteger

In the literature; extensive work on the q and (p,q)-calculus has contributed greatly to describing the different generalizations of many operators involving the q and (p,q)-integers. In this study, we will present to you, that we define Gamma type operator based on (p,q)-integer. We get some direct output including asymptotic formula and error estimation in terms of modulus continuity. In addition, as a result of the research, we estimate the convergence rate of these operators in a weighted space.

PDF

___

Acar, T., 2016. (p,q)-generalization of Szàsz--Mirakyan operators. Math. Method. Appl.Sci., 39(10), 2685-2695.
Acar, T., Mohiudine, S. A., Mursaleen, M., 2018. Approximation by (p,q)-Baskakov-Durrmeyer--Stancu operators. Complex Analysis and Operator Theory, 12(6), 1453-1468.
Altomare, F. and Campiti, M., 1994. Korovkin Type Approximation Theory and its Applications,17, Walter de Gruyter, Berlin.
Aral, A. and Gupta, V., 2016. Bernstein Durrmeyer operators based on two parameters. Facta Unıversıtatıs (Nıs) Ser. Math. Inform., 31(1), 79–95.
Gupta, V., Noor M. A, and Beniwal, M.S., 2006. Rate of convergence in simultaneous approximation for Szàsz---Mirakyan---Durrmeyer operators. J. Math. Anal. Appl., 322(2), 964—970.
Gupta, V., 2018. (p,q)-Szàsz---Mirakyan---Baskakov operators, Complex Analysis and Operator Theory. 12(1), 17-25.
Karaisa, A., Tollu D. T., and Asar, Y., 2015. Stancu type generalization of q-Favard-Szàsz operators. Appl. Math. Comput., 264, 249-257.
Karaisa, A., 2016. Approximation by Durrmeyer type Jakimoski--Leviatan operators. Math. Methods Appl. Sci., 39, 2401-2410.
Karsli, H., 2007. Rate of convergence of a new gamma type operators for functions with derivatives of bounded variation. Math. Comput. Model., 45(5-6), 617-624.
Karsli, H. and Özarslan M. A., 2010. Direct local and global approximation results for the operators of gamma type. Hacet. J. Math. Stat., 39 (2), 241-253.
Karsli, H., Agrawal P. N., and Goyal, M., 2015. General Gamma type operators based on q-integers. Applied Mathematics and Computation, 251, 564-575.
Khursheed Ansaria J., and Karaisa, A., 2017. On the approximation by Chlodowsky type generalization of (p, q)-Bernstein operators. Int. J. Nonlinear Anal. Appl,. 8(2), 181-200.
Mao, L.C., 2007. Rate of convergence of Gamma type operatör. J. Shangqiu Teachers Coll., 12, 49-52.
Mursaleen, M., Nasiuzzaman, Md., and Nurgali, A., 2015. Some approximation results on Bernstein-Schurer operators defined by (p,q)-integers. Jou. Ineq. Appl., 249(2015).
Sadjang, P. N., 2018. On the fundamental theorem of (p,q)-calculus and some (p,q)-Taylor formulas. Results Math, 73, 21-39.