Hill Publishing Group | contact@hillpublisher.com

Hill Publishing Group

Location:Home / Journals / Journal of Applied Mathematics and Computation /


Approximation by Differences on Some Mixed Summation-Integral Type Operators

Date: June 2,2022 |Hits: 182 Download PDF How to cite this paper

Prerna Sharma

Department of Basic Science, Sardar Vallabh Bhai Patel University of Agriculture and Technology, Meerut, Uttar Pradesh, India.

*Corresponding author: Prerna Sharma


This paper is the study of two different general linear positive operators defined on unbounded interval. Here we introduce a generalized family of the hybrid integral operators. The special cases of our operators include some well known integral operators. The main aim of the present note is to prevent the researchers to study individual operators, and by this form they can study the approximation properties of any linear positive operator by differences of other forms of the same operator. We obtain estimates for the difference of these operators namely Lupas operators in quantitative form. We study quantitative estimates for the difference of generalized Lupas-Szasz and generalized Lupas-Kantorovich operators. Finally, we obtain the quantitative estimate in terms of the weighted modulus of smoothness for these operators. Also, their mutual differences are possible, which are estimated in the present paper. Here, we obtain a new approach to find the moments using the concept of moment generating functions.


[1] Agarwal, R. P. and Gupta, V. (2012). On q-analogue of a complex summation integral type operators in compact disks. J. Ineq.. Appl., 2012(1), Art 111. 

[2] Gupta, V. and Maheshwari, P. (2019). Approximation with certain Post-Widder operators. Publications De L’institut Mathematiqu e, 105(119), 131-136. 

[3] Sharma, P. M. (2021). Iterative combinations for Srivastava-Gupta operators. Asian European J. of Math., 14(7), 2150108, p. 10.

[4] Sharma, P. M. (2015). On Modified Srivastava-Gupta Operators. Filomat, 29: 6, 1173-1177. 

[5] Sharma, P. M. and Abid, M. (2020) Approximation by (p,q) Szász-Beta-Stancu operators, Arab. J. Math., 9, 191-200. 

[6] Maheshwari, P. and Sharma, D. (2012). Approximation by q-Baskakov-Beta-Stancu operators. Rend. Circ. Mat. Palerm, 61, 297-305.  

[7] Sharma, P. (2021). Statistical convergence estimates for (p,q)-Baskakov-Durrmeyer type operators. Nepal J. of Math. Sciences, 2(2), 125-130.

[8] Aral, A., Inoan, D., and Rasa, I. (2019). On difference of linear positive operators. Analy. And Math. Phy., 9, 1227-1239.

[9] Acu, M., Tunca, G., and Rasa, I. (2021). Difference of positive linear operators on surplices. J. of functional spaces, p. 11. http://doi.org/10.1155/2021/5531577. 

[10] Gupta, V. and Tachev, G. (2019). A note on difference of two linear positive operators. Constru. Math. Analy., 2(1), 1-7. 

[11] Aral, A. and Gupta, V. (2016). Direct estimates for Lupas Durrmeyer operators. Filomat, 30, 191-199.

[12] Lupas, A. (1995). The approximation by means of some linear positive operators. Math. Research, 86, 201-230.

[13] Abel, U. and Ivan, M. (2007). On a generalization of an approximating operator defined by A. Lupas. General Math., 15, 21-34. 

[14] Lain, B. Y. (2017). Approximation properties of the modified Lupas-Kantorovich type operators. MATEC Web of Conferences, 139, 00091. DOI: 10.1051/matecconf/20171390009.

[15] Gupta, V., Rassias, T. M., and Pandey, E. (2017). On genuine Lupas-Beta operators and modulus of continuity. Int. J. Nonlinear Anl. And Appl., 8(1), 23-32. 

[16] Qasim, M., Khan, A., and Abbas, Z. (2021). A new construction of Lupas operators and its approximation proper-ties. Advances in Diff. Eqs., 51. http://doi.org/10/1186/s13662-020-03143-5.

[17] Agratini, O. (1999). On a sequence of linear positive operators. Facta Universitatis (Nis), Ser. Math. Inform., 14, 41-48.

[18] Gupta, V. (2019). On difference of operators with applications to Szasz type operators. Rivista de. La. Real Aca. De. Cie. Exactas, Fiscas Y, Naturales. Series A. mate., 113, 2059-2071.

How to cite this paper

Approximation by Differences on Some Mixed Summation-Integral Type Operators

How to cite this paper:  Prerna Sharma. (2022) Approximation by Differences on Some Mixed Summation-Integral Type Operators. Journal of Applied Mathematics and Computation6(2), 230-234.

DOI: http://dx.doi.org/10.26855/jamc.2022.06.007

Volumes & Issues

Free HPG Newsletters

Add your e-mail address to receive free newsletters from Hill Publishing Group.

Contact us

Hill Publishing Group

8825 53rd Ave

Elmhurst, NY 11373, USA

E-mail: contact@hillpublisher.com

Copyright © 2019 Hill Publishing Group Inc. All Rights Reserved.