The convergence of implicit Mann and Ishikawa iterations for weak generalized φ-hemicontractive mappings in real Banach spaces
Zhiqun Xue, Fang Zhang · Journal of Inequalities and Applications · 2013
Let E be a real Banach space and let D be a nonempty closed convex subset of E, let be a continuous weak generalized φ-hemicontractive mapping. The existence theorem of a fixed point of a weak generalized φ-pseudocontractive mapping is obtained. And we also prove that implicit Mann and Ishikawa iterations converge strongly to the unique fixed point of T. Our results extend the corresponding results of Xiang (Nonlinear Anal. 70(6): 2277-2279, 2009). MSC:47H09, 47J25.