A NEW KIND OF THE VARIANT OF THE MODIFIED BERNSTEIN-KANTOROVICH
OPERATORS DEFINED BY ¨OZARSLAN AND DUMAN
Abstract
In the present article, we dene a new kind of the modified
Bernstein-Kantorovich operators defined by ¨ Ozarslan
(https://doi.org/10.1080/01630563.2015.1079219) i.e. we introduce a new
function ς(x) in the modified Bernstein-Kantorovich operators defined by
Ozarslan with the property ({) is an infinitely differentiable function
on [0; 1]; ς(0) = 0; ς(1) = 1 and ς’(x) > 0 for all x∈
[0; 1]. We substantiate an approximation theorem by using of the
Bohman-Korovkins type theorem and scrutinize the rate of convergence
with the aid of modulus of continuity, Lipschitz type functions for the
our operators and the rate of convergence of functions by means of
derivatives of bounded variation are also studied. We study an
approximation theorem with the help of Bohman-Korovkins type theorem in
A-Statistical convergence. Lastly, by means of a numerical example, we
illustrate the convergence of these operators to certain functions
through graphs with the help of MATHEMATICA and show that a careful
choice of the function ς(x) leads to a better approximation results as
compared to the modified Bernstein-Kantorovich operators defined by
Ozarslan (https://doi.org/10.1080/01630563.2015.1079219).