Abstract
The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.
Highlights
By C [0, 1], we denote the space of continuous functions defined on [0, 1], and by
Let N be the set of all positive integers
With the results introduced by King, a new direction of research was initiated, which concerns the construction of new operators with better approximation properties, obtained by modifying existing sequences of linear positive operators
Summary
By C [0, 1], we denote the space of continuous functions defined on [0, 1], and by. L1 [0, 1], the space of all functions defined on [0, 1], which are Lebesgue integrable. In [10], J.P. King introduced a new class of positive linear Bernstein-type operators which reproduce constant functions (e1 ( x )) and e2 ( x ). King introduced a new class of positive linear Bernstein-type operators which reproduce constant functions (e1 ( x )) and e2 ( x ) These operators are a generalization of the Bernstein operators, but they are not polynomial-type operators. With the results introduced by King, a new direction of research was initiated, which concerns the construction of new operators with better approximation properties, obtained by modifying existing sequences of linear positive operators. This subject has been one of great interest.
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