Error estimation for ill-posed problems on piecewise convex functions and sourcewise represented sets.

In this paper solutions of ill-posed problems with some a priori information about the exact solution are considered. For the first group of such problems it is supposed that the exact solution is a bounded piecewise convex function on some bounded segment [ a, b]. It is shown that the set of these functions is a compact set in LP[ a, b] and an approximate solution tends to the exact one uniformly on some subset of [ a, b]. Sourcewise represented functions form the second group of the problems. For this case it is possible to find a so-called a posteriori error estimation of an approximate solution. The method of extending compacts may help to estimate this a posteriori error. [ABSTRACT FROM AUTHOR]