Solution of ill-posed problems on sets of functions convex along all lines parallel to coordinate axes

In the paper we consider linear ill-posed problems on sets of functions convex upwards or downwards along all lines that belong to a functions' domain and are parallel to coordinate axes. A regularizing algorithm is constructed such that an approximate solution tends to the exact one uniformly of some subsets of the domain. The algorithms to estimate an error of finite dimensional approximation and to find a lower and an upper functions that bound all approximation solutions are provided. As a model example, an inverse problem for a two-dimensional heat conduction equation is solved. © 2008 de Gruyter.