LAVRENTIEV REGULARIZATION OF NONLINEAR ILL-POSED EQUATIONS UNDER GENERAL SOURCE CONDITION - Mahale, P.; Nair, M. T. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
Analogues to the procedure adopted by Scherzer et.al (1993) for choosing the regularization parameter in Tikhonov regularization of nonlinear ill-posed equations of the form F(x) = y, Tautenhahn (2002) considered an a posteriori parameter choice strategy for Lavrentiev regularization, and derived order optimal error estimates under Holder type source conditions. In this paper, we derive order optimal error estimates under a general source condition so that the results are applicable for both mildly and exponentially ill-posed problems. Results in this paper generalize results of Tautenhahn (2002) and also extend results of Nair and Tautenhahn (2004) to the nonlinear case.