Quasi-solution of the ill-posed problem

We assume now that the problem (2.14) is conditionally well-posed (Tikhonov s well-posed). Let us assume, also, that the right-hand side of (2.14) is given with some error  

Obviously, we can reach the minimum of the /ry(/lm,d ) in C, if the correctness set is a compact. In this case the quasi-solution exists for any data d.  

Subset AC of the data space D is an image of the correctness set C obtained as a result of the application of operator A. A quasi-solution, m, is selected from the correctness set C under the condition that its image, A (m ), is the closest element in the subset AC to the observed noisy data, d.  

It can be proved also that the quasi-solution is a continuous function of d. Indeed, let us consider the triangle inequality 

According to the definition of the quasi-solution and condition (2.18), it follows from inequality (2.21) that 

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