Uniform regularization of the problem of calculating the values of an operator

Abstract

Let X and Y be linear normed spaces, W a set in X, A an operator from W into Y, and\(\mathfrak{W}\) the set of all operators or the set ℒ of linear operators from X into Y. With δ>0 we put $$v\left( {\delta ,\mathfrak{M}} \right) = \mathop {\inf }\limits_{T \in \mathfrak{M}} \mathop {\sup }\limits_{x \in W} \mathop {\sup }\limits_{\left\| {\eta - x} \right\|_X \leqslant \delta } \left\| {Ax - T\eta } \right\|_Y $$ .