Paltanea Type Theorems on Estimation by Positive Discrete Functionals

The article is devoted to inequalities of the type \(\left|F\left(f\right)-F\left({e}_{0}\right)f\left(x\right)\right|\le F\left({e}_{0}\right){\omega }_{2}\left(f,h\right),\) $$\left|F,\left(f\right),-,F,\left(e_0\right),f,\left(x\right)\right|\le F\left(e_0\right){\omega }_2\left(f,,,h\right),$$

where F is a functional of the form \(F\left(f\right)=\sum_{y\in Y}\gamma \left(y\right)f\left(y\right)\) $F\left(f\right)={\sum }_{y\in Y}\gamma \left(y\right)f\left(y\right)$ , and Y is an at most countable set with no accumulation points on \({\mathbb{R}}\) $\mathbb{R}$ , γ : Y → (0, ∞).