Strong convergence to fixed points of non-Lipschitzian mappings

In this paper, we first show the strong convergence of the modified Moudafi iteration process when E is a real uniformly convex Banach space, S is AQT self-mapping and T is ANI self-mapping satisfying Condition (B). Next, we show the strong convergence of the modified Mann iteration process when T is ANI self-mapping satisfying Condition (A), which generalizes the result due to Kim (J. Nonlinear Convex Anal. 13(3):449–457, 2012). Finally, we show the strong convergence of the Schu iteration process when T is ANI self-mapping satisfying Condition (A), which generalizes the result due to Rhoades (J. Math. Anal. Appl. 183:118–120, 1994). [Figure not available: see fulltext.]. © 2013, The Author(s).