Convergence and Difference Estimates Between Mastroianni and Gupta Operators


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Authors: NEHA AND N. DEO

DOI: 10.46793/KgJMat2302.259D

Abstract:

Gupta operators are a modified form of Srivastava-Gupta operators and we are concerned about investigating the difference of operators and we estimate the difference of Mastroianni operators with Gupta operators in terms of modulus of continuity of first order. We also study the weighted approximation of functions and obtain the rate of convergence with the help of the moduli of continuity as well as Peetre’s K-functional of Gupta operators.



Keywords:

Mastroianni operator, modulus of continuity, Gupta operator.



References:

[1]   U. Abel, V. Gupta and M. Ivan, Asymptotic approximation of functions and their derivatives by generalized Baskakov-Szász-Durrmeyer operators, Anal. Theory Appl. 21(1) (2005), 15–26. https://doi.org/10.1007/BF02835246

[2]   A. M. Acu and C. V. Muraru, Certain approximation properties of Srivastava-Gupta operators, J. Math. Inequal. 12(2) (2018), 583–595. https://doi.org/10.7153/jmi-2018-12-44

[3]   A. M. Acu and I. Raşa, New estimates for the differences of positive linear operators, Numer. Algorithms 73 (2016), 775–789. https://doi.org/10.1007/s11075-016-0117-8

[4]   A. Aral, D. Inoan and I. Raşa, On differences of linear positive operators, Anal. Math. Phys. 9 (2019), 1227–1239. https://doi.org/10.1007/s13324-018-0227-7

[5]   D. Barbosu and N. Deo, Some Bernstein-Kantorovich operators, Automat. Comput. Appl. Math. 22(1) (2013), 15–21.

[6]   D. Barbosu and D. Miclăuş, On the Voronovskaja-type formula for the Bleimann, Butzer and Hahn bivariate operators, Carpathian J. Math. 33(1) (2017), 35–42.

[7]   N. Deo, Voronovskaya type asymptotic formula for Lupaş-Durrmeyer operators, Rev. Un. Mat. Argentina 48(1) (2007), 47–54.

[8]   N. Deo, A note on equivalent theorem for Beta operators, Mediterr. J. Math. 4(2) (2007), 245–250. https://doi.org/10.1007/s00009-007-0115-0

[9]   N. Deo and N. Bhardwaj, Some approximation results for Durrmeyer operators, Appl. Math. Comput. 217(12) (2011), 5531–5536. https://doi.org/10.1016/j.amc.2010.12.026

[10]   N. Deo, Faster rate of convergence on Srivastava-Gupta operators, Appl. Math. Comput. 218(21) (2012), 10486–10491. https://doi.org/10.1016/j.amc.2012.04.012

[11]   N. Deo and M. Dhamija, Generalized positive linear operators based on PED and IPED, Iran. J. Sci. Technol. Trans. A Sci. 43 (2019), 507–513. https://doi.org/10.1007/s40995-017-0477-5

[12]   N. Deo and R. Pratap, The family of Szász-Durrmeyer type operators involving Charlier polynomials, Kragujevac J. Math. (2023) (to appear).

[13]   T. Garg, P. N. Agrawal and A. Kajla, Jain-Durrmeyer operators involving inverse Polya-Eggenberger distribution, Proc. Nat. Acad. Sci. India Sect. A 89 (2019), 547–557. https://doi.org/10.1007/s40010-018-0492-8

[14]   I. Gavrea and M. Ivan, Asymptotic behaviour of the iterates of positive linear operators, Abstr. Appl. Anal. (2011). https://doi.org/10.1155/2011/670509

[15]   V. Gupta, On difference of operators with applications to Szász type operators, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(3) (2019), 2059–2071. https://doi.org/10.1007/s13398-018-0605-x

[16]   V. Gupta, Some examples of Genuine approximation operators, General Math. 26(1-2) (2018), 3–9.

[17]   V. Gupta, Difference of operators of Lupaş type, Constructive Mathematical Analysis 1(1) (2018), 9–14. https://doi.org/10.33205/cma.452962

[18]   V. Gupta and R. P. Agarwal, Convergence Estimates in Approximation Theory, Springer, Switzerland AG, 2014. https://doi.org/10.1007/978-3-319-02765-4

[19]   V. Gupta, T. M. Rassias, P. N. Agrawal and A. M. Acu, Recent Advances in Constructive Approximation Theory, Springer Optimization and Its Applications 138, Springer, Cham, 2018. https://doi.org10.1007/978-3-319-92165-5

[20]   N. Ispir, On modified Baskakov operators on weighted spaces, Turkish J. Math. 25(3) (2001), 355–365.

[21]   N. Ispir and C. Atakut, Approximation by modified Szász-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci. 112(4) (2002), 571–578.

[22]   E. Ibikli and E. A. Gadjieva, The order of approximation of some unbounded function by the sequences of positive linear operators, Turkish J. Math. 19(3) (1995), 331–337.

[23]   A. J. López-Moreno and J. M. Latorre-Palacios, Localization results for generalized Baskakov/Mastroianni and composite operators, J. Math. Anal. appl. 380(2) (2011), 425–439. https://doi.org/10.1016/j.jmaa.2011.03.060

[24]   N. Malik, Some approximation properties for generalized Srivastava-Gupta operators, Appl. Math. Comput. 269 (2015), 747–758. https://doi.org/10.1016/j.amc.2015.07.113

[25]   N. S. Mishra and N. Deo, Kantorovich Variant of Ismail-May Operators, Iran. J. Sci. Technol. Trans. A Sci. 44 (2020), 739–748. https://doi.org/10.1007/s40995-020-00863-x

[26]   T. Neer, N. Ispir and P. N. Agrawal, Bezier variant of modified Srivastava-Gupta operators, Rev. Un. Mat. Argentina 58(2) (2017), 199–214.

[27]   M. A. Özarslan and H. Aktŭglu, Local approximation for certain King type operators, Filomat 27 (2013), 173–181. https://doi.org/0.2298/FIL1301173O

[28]   R. Pratap and N. Deo, Approximation by genuine Gupta-Srivastava operators, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 113(3) (2019), 2495–2505. https://doi.org/10.1007/s13398-019-00633-4

[29]   H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37 (2003), 1307–1315. https://doi.org/10.1016/S0895-7177(03)90042-2