Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D, in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini- tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides...