Approximation of modified Favard Szasz-Mirakyan operators of maximum-product type ∗
DOI:
https://doi.org/10.48165/Keywords:
Max-product, modified Favard Szasz–Mirakyan operators, degree of ap proximation, nonlinear operatorsAbstract
Nonlinear positive operators by means of maximum and product were intro duced by B. Bede. In this paper, we introduce nonlinear maximum-product type modified Favard Szasz–Mirakyan operators. Our main purpose is to give a theorem on the rate of convergence.
References
Acar, E., Karahan, D. and Serenbay, S.K. (2020). Approximation for the Bernstein operator of max-product kind in symmetric range, Khayyam J. Math., 6(2), 257–273.
Bede, B., Coroianu, L. and Gal, S.G. (2010). Approximation and shape preserving properties of the nonlinear Favard Szasz–Mirakyan operator of max-product kind, Filomat, 24(3), 55–72. [3] Bede, B., Coroianu, L. and Gal, S.G. (2011). Approximation by truncated Favard Szasz–Mirakyan operator of max-product kind, Demonstratio Mathematica, 44(1), 105–122.
Bede, B., Coroianu, L. and Gal, S.G. (2016). Approximation by Max-Product Type Operators, Springer International Publishing, Switzerland.
Becker, M., Kucharski, D. and Nessel, R.J. (1978). Global approximation theorems for the Szász Mirakyan operators in exponential weight spaces, Linear Spaces and Approximation (Proc. Conf. Oberwolfach, 1977), Birkhäuser Verlag, Basel, Internat. Series of Num. Math., 40 , 319–333.
Güngör, Y. and Ispir, N. (2016). Quantitative estimates for generalized Szasz operators of max product kind, Results Math., 70(3–4), 447–456.
Ispir, N. and Atakut, C. (2002). Approximation by modified Favard Szasz–Mirakyan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci., 112(4), 571–578.
Rempulska, L. and Walczak, Z. (2001). Approximation properties of certain modified Favard Szasz-Mirakyan operators, Le Matematiche (Catania), 55(1), 121–132.
Serenbay, S.K. and Dalmanoğlu, Ö (2017). Rate of convergence for generalized Szasz-Mirakyan operators in exponential weighted space, Appl. Appl. Math., 12(2), 884–897. [10] Walczak, Z. (2002). On approximation by modified Favard Szasz-Mirakyan operators, Glasnik Matematicki, 37(2), 303–319.