Ivan Gadjev
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View article: Higher Order Approximation of Continuous Functions by a Modified Meyer-König and Zeller-Type Operator
Higher Order Approximation of Continuous Functions by a Modified Meyer-König and Zeller-Type Operator Open
A new Goodman-Sharma type modification of the Meyer-König and Zeller operator for approximation of bounded continuous functions on [0,1) is presented. We estimate the approximation error of the proposed operator and prove direct and strong…
View article: On a New Modification of Baskakov Operators with Higher Order of Approximation
On a New Modification of Baskakov Operators with Higher Order of Approximation Open
A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on [0,∞). We study the approximation error of the proposed operator. Our main results are a direct theorem a…
View article: Higher order approximation of functions by modified Goodman-Sharma operators
Higher order approximation of functions by modified Goodman-Sharma operators Open
Here we study the approximation properties of a modified Goodman-Sharma operator recently considered by Acu and Agrawal in [1]. This operator is linear but not positive. It has the advantage of a higher order of approximation of functions …
View article: On a New Modification of Baskakov Operators with Higher Order of Approximation
On a New Modification of Baskakov Operators with Higher Order of Approximation Open
A new Goodman-Sharma modification of the Baskakov operator is presented for approximation of bounded and continuous on $[0,\,\infty)$ functions. In our study on the approximation error of the proposed operator we prove direct and strong co…
View article: Higher Order Approximation of Functions by Modified Goodman-Sharma Operators
Higher Order Approximation of Functions by Modified Goodman-Sharma Operators Open
Here we study the approximation properties of a modified Goodman-Sharma operator recently considered by Acu and Agrawal in 2019. This operator is linear but not positive. It has the advantage of a higher order of approximation of functions…
View article: Sharp Hardy’s inequalities in Hilbert spaces
Sharp Hardy’s inequalities in Hilbert spaces Open
We study the behavior of the smallest possible constants d(a,b) and d_{n} in Hardy’s inequalities \int_{a}^{b}\biggl(\frac{1}{x}\int_{a}^{x}f(t)dt\biggr)^{2}\:dx\leq d(a,b){}\int_{a}^{b} [f(x)]^{2}\: dx and \sum_{k=1}^{n}\Big(\frac{1}{k}\s…
View article: On the Constants and Extremal Function and Sequence for Hardy Inequalities in $L_p$ and $l_p$
On the Constants and Extremal Function and Sequence for Hardy Inequalities in $L_p$ and $l_p$ Open
We study the behavior of the smallest possible constants $d(a,b)$ and $d_n$ in Hardy inequalities $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^p\,dx\leq d(a,b)\,\int_a^b [f(x)]^p dx $$ and $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{…
View article: Hardy’s inequalities in finite dimensional Hilbert spaces
Hardy’s inequalities in finite dimensional Hilbert spaces Open
We study the behaviour of the smallest possible constants $d_n$ and $c_n$ in Hardy's inequalities $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a_k^2, \qquad (a_1,\ldots,a_n) \in \mathbb{R}^n $$ and $$ \i…
View article: Weighted approximation by Kanotrovich type modification of Meyer-König and Zeller operator
Weighted approximation by Kanotrovich type modification of Meyer-König and Zeller operator Open
We investigate the weighted approximation of functions in $L_p$-norm by Kantorovich modifications of the classical Meyer-König and Zeller operator, with weights of type $(1-x)^\alpha, \alpha \in \mathbb{R}$. By defining an appropriate K-fu…
View article: Weighted approximation by Baskakov operators
Weighted approximation by Baskakov operators Open
The weighted approximation errors of Baskakov operator is characterized for weights of the form w(x) = x γ 0 (1 + x) γ∞ , where γ 0 ∈ [-1,0] , γ ∞ ∈ R .Direct inequalities and strong converse inequalities of type A are proved in terms of t…