@article{Argyros_George_2013, title={EXPANDING THE APPLICABILITY OF A TWO STEP NEWTON LAVRENTIEV METHOD FOR ILL-POSED PROBLEMS}, volume={4}, url={http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/242}, abstractNote={<p>In [3] we presented a cubically convergent Two Step Directional NewtonMethod (TSDNM) for approximating a solution of an operator equation in a Hilbert space setting. George and Pareth in [13] use the analogous Two Step Newton Lavrentiev Method (TSNLM) to approximate a solution of an ill-posed equation. In the present paper we show how to expand the applicability of (TSNLM). In particular, we present a semilocal convergence analysis of (TSNLM) under: weaker hypotheses, weaker convergence criteria, tighter error estimates on the distances involved and an at least as precise information on the location of the solution.</p>}, number={2}, journal={Journal of Nonlinear Analysis and Optimization: Theory & Applications}, author={Argyros, I. and George, S.}, year={2013}, month={Jul.}, pages={1-15} }