TY - JOUR AU - Aliaga, Edmond AU - Rexhepi, Shpetim PY - 2022 TI - Degree of approximation for bivariate extension of blending type \(q\)-Durrmeyer operators based on Pólya distribution JO - Journal of Mathematics and Computer Science SP - 256--272 VL - 24 IS - 3 AB - In this paper we introduce a bivariate of \(q\)-Durrmeyer variant of generalized Bernstein operators by using Pólya distribution. The convergence rate of these operators is examined by means of the Lipschitz class and the modulus of continuity. Furthermore, we obtain a Voronovskaja type symptotic formula, error estimation in terms of the partial modulus of continuity and Peetre's K-functional. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.024.03.07 DO - 10.22436/jmcs.024.03.07 ID - Aliaga2022 ER - TY - JOUR TI - The approximation of bivariate Chlodowsky-Szasz-Kantorovich-Charlier-type operators AU - P. N. Agrawal AU - B. Baxhaku AU - R. Chauhan JO - J. Inequal. Appl. PY - 2017 DA - 2017// VL - 2017 ID - Agrawal2017 ER - TY - JOUR TI - On the q analogue of Stancu-beta operators AU - A. Aral AU - V. Gupta JO - Appl. Math. Lett. PY - 2012 DA - 2012// VL - 25 ID - Aral2012 ER - TY - BOOK TI - Applications of q-Calculus in Operator Theory AU - A. Aral AU - V. Gupta AU - R. P. Agarwal PB - Springer PY - 2013 DA - 2013// CY - New York ID - Aral2013 ER - TY - JOUR TI - Some bivariate Durrmeyer operators based on q-integers AU - D. Barbosu AU - C. V. Muraru AU - A.-M. Acu JO - J. Math. Inequal. PY - 2017 DA - 2017// VL - 11 ID - Barbosu2017 ER - TY - JOUR TI - Degree of approximation for bivariate extension of Chlodowsky-type q-Bernstein-StancuKantorovich operators AU - B. Baxhaku AU - P. N. Agrawal JO - Appl. Math. Comput. PY - 2017 DA - 2017// VL - 306 ID - Baxhaku2017 ER - TY - BOOK TI - Semi-groups of operators and approximation AU - P. L. Butzer AU - H. Berens PB - Springer PY - 2013 DA - 2013// CY - Berlin ID - Butzer2013 ER - TY - JOUR TI - Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q-integers AU - O. Dogru AU - V. Gupta JO - Georgian Math. J., PY - 2005 DA - 2005// VL - 12 ID - Dogru2005 ER - TY - JOUR TI - Some approximation properties of q-Durrmeyer operators AU - V. Gupta JO - Appl. Math. Comput., PY - 2008 DA - 2008// VL - 197 ID - Gupta2008 ER - TY - JOUR TI - Bernstein Durrmeyer operators based on two parameters AU - V. Gupta AU - A. Aral JO - Facta Univ. Ser. Math. Inform. PY - 2016 DA - 2016// VL - 31 ID - Gupta2016 ER - TY - JOUR TI - q-Durrmeyer operators based on Polya distribution AU - V. Gupta AU - T. M. Rassias AU - H. Sharma JO - J. Nonlinear Sci. Appl. PY - 2016 DA - 2016// VL - 9 ID - Gupta2016 ER - TY - JOUR TI - Quantitative estimates for a certain bivariate Chlodowsky-Szasz-Kantorovich type operators AU - N. Ispir AU - I. Buyukyazıcı JO - Math. Commun. PY - 2016 DA - 2016// VL - 21 ID - Ispir2016 ER - TY - JOUR TI - A q-analogue of the Bernstein operator, Seminar on Numerical and Statistical Calculus AU - A. Lupas JO - Univ. ”Babes¸- Bolyai”, Cluj-Napoca PY - 1987 DA - 1987// VL - 1987 ID - Lupas1987 ER - TY - JOUR TI - Some approximation properties of q-Durrmeyer-Schurer operators AU - C. V. Muraru AU - A. M. Acu JO - Sci. Stud. Res. Ser. Math. Inform. PY - 2013 DA - 2013// VL - 23 ID - Muraru2013 ER - TY - JOUR TI - Approximation properties for generalized q-Bernstein polynomials AU - G. Nowak JO - J. Math. Anal. Appl. PY - 2009 DA - 2009// VL - 350 ID - Nowak2009 ER - TY - JOUR TI - Bernstein polynomials based on the q-integers AU - G. M. Phillips JO - Ann. Numer. Math. PY - 1997 DA - 1997// VL - 4 ID - Phillips1997 ER - TY - JOUR TI - GBS operators of bivariate Bernstein-Durrmeyer-type on a triangle AU - R. Ruchi AU - B. Baxhaku AU - P. N. Agrawal JO - Math. Methods Appl. Sci., PY - 2018 DA - 2018// VL - 41 ID - Ruchi2018 ER - TY - JOUR TI - Approximation of functions by a new class of linear polynomial operators AU - D. D. Stancu JO - Rev. Roumaine Math. Pures Appl. PY - 1968 DA - 1968// VL - 13 ID - Stancu1968 ER - TY - JOUR TI - On the convergence of a sequence of linear positive operators in the space of continuous funtions of two variables AU - I. V. Volkov JO - Dokl. Akad. Nauk SSSR, PY - 1957 DA - 1957// VL - 115 ID - Volkov1957 ER -