Uniform regularization of the problem of calculating the values of an operator
Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 231-244.

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Let $X$ and $Y$ be linear normed spaces, $W$ a set in $X$, $A$ an operator from $W$ into $Y$, and $\mathfrak M$ the set $\mathfrak G$ of all operators or the set $\mathscr L$ of linear operators from $X$ into $Y$. With $\delta\ge0$ we put $$ \nu(\delta,\mathfrak M)=\inf_{T\in\mathfrak M}\sup_{x\in W}\sup_{\|\eta-x\|_X\le\delta}\|Ax-T\eta\|_Y. $$ We discuss the connection of $\nu(\delta,\mathfrak M)$ with the Stechkin problem on best approximation of the operator $A$ in $W$ by linear bounded operators. Estimates are obtained for $\nu(\delta,\mathfrak M)$ e.g., we write the inequality, where $H(Y)$ is Jung's constant of the space $Y$, and $\Omega(t)$ is the modulus of continuity of $A$ in $W$.
@article{MZM_1977_22_2_a7,
     author = {V. V. Arestov},
     title = {Uniform regularization of the problem of calculating the values of an operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {231--244},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a7/}
}
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V. V. Arestov. Uniform regularization of the problem of calculating the values of an operator. Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 231-244. http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a7/