Sharp upper and lower bounds for the moments of Bernstein polynomials

Approximation properties of a certain modification of Durrmeyer operators

“…It is known that (see [8], [24], [25])at a point x of continuity of f there holds the limit lim n→∞ B n (f )(x) = f (x). These operators have been widely studied by researchers( [1], [3], [5], [9], [29]). Interesting properties of these operators include, shape preservation, uniform approximation, numerical quadrature, possibility of approximation of derivatives f (s) of a differentiable function f by the corresponding derivative (B n (f )) (s) etc.…”

Approximation Properties of a Certain Modification of Durrmeyer Operators

“…It is known that (see [8], [24], [25])at a point x of continuity of f there holds the limit lim n→∞ B n (f )(x) = f (x). These operators have been widely studied by researchers( [1], [3], [5], [9], [29]). Interesting properties of these operators include, shape preservation, uniform approximation, numerical quadrature, possibility of approximation of derivatives f (s) of a differentiable function f by the corresponding derivative (B n (f )) (s) etc.…”