General source conditions for nonlinear ill-posed equations

In order to derive error estimates for regularized approximate solutions of ill-posed equations F(x)=y, where F : D(F)XY is a nonlinear operator between Hilbert spaces X and Y, certain source conditions are to be imposed on the unknown solution [image omitted]. For linear ill-posed equations of the form Ax=y, where A:XY is a bounded linear operator, Nair, Schock, and Tautenhahn considered a general source condition, namely, [image omitted]M, :={[(A*A)]1/2v: v}, where the function is general enough to include some of the well-studied special cases. We extend such procedure to the nonlinear ill-posed equations F(x)=y, so that it also includes the results of Tautenhahn where the special case of ():=/2 is considered.