Jain-Baskakov Operators and its Different Generalization

被引:10
作者
Patel P. [1 ,2 ]
Mishra V.N. [3 ]
机构
[1] Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, 395 007, Gujarat
[2] Department of Mathematics, St. Xavier’s College (Autonomous), Ahmedabad, 380 009, Gujarat
[3] L. 1627 Awadh Puri Colony Beniganj, Phase -III, Opposite - Industrial Training Institute (I.T.I.), Ayodhya Main Road, Faizabad, 224 001, Uttar Pradesh
关键词
A-Statistical convergence; Baskakov operators; Jain operators; King-type operators; Rate of convergence; Stancu operators; Weighted approximation;
D O I
10.1007/s40306-014-0077-9
中图分类号
学科分类号
摘要
The aim of this work is to introduce a new sequence of positive linear operators, which is an integral version of Jain operators. We studied some direct results in ordinary approximation. Weighted approximation, rate of convergence, and A-statistical convergence are investigated. Also, we discussed approximation properties of King-type and Stancu-type generalization of these new sequences of linear positive operators and investigated a modification of Jain-Baskakov operators with parameter c. At the end, we propose a q-analogue of Jain operators based on a q-integer. © 2014, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
引用
收藏
页码:715 / 733
页数:18
相关论文
共 29 条
[11]  
Gadjiev A.D., Efendiyev R.O., Ibikli E., On Korovkin type theorem in the space of locally integrable functions, Czechoslov. Math. J., 53, 1, pp. 45-53, (2003)
[12]  
Gupta V., Approximation for modified Baskakov Durrmeyer type operators. Rocky Mountain, J. Math., 39, 3, pp. 1-17, (2009)
[13]  
Gupta V., Deo N., A note on improved estimations for integrated Szász-Mirakyan operators, Math. Slovaca, 61, 5, pp. 799-806, (2011)
[14]  
Gupta V., Srivastava G., Sahai A., On simultaneous approximation by Szasz Beta operators, Soochow J. Math., 21, 1, pp. 1-11, (1995)
[15]  
Gupta V., Verma D.K., Agrawal P.N., Simultaneous approximation by certain Baskakov-Durrmeyer-Stancu operators, J. Egypt. Math. Soc., 20, pp. 183-187, (2012)
[16]  
Ibrahim B., Approximation by Stancu-Chlodowsky polynomials, Comput. Math. Appl., 59, 1, pp. 274-282, (2010)
[17]  
Jain G.C., Approximation of functions by a new class of linear operators, J. Aust. Math. Soc., 13, 3, pp. 271-276, (1972)
[18]  
Kac V.G., Cheung P., Quantum Calculus. Universitext. Springer, New York, x+112 pp, (2002)
[19]  
King J.P., Positive linear operators which preserve x <sup>2</sup> , Acta Math. Hung., 99, 3, pp. 203-208, (2003)
[20]  
Korovkin P.P., On convergence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR, 90, pp. 961-964, (1953)