ON THE ON THE CONVERGENCE BETWEEN THE MANN ITERATION AND ISHIKAWA ITERATION FOR THE GENERALIZED LIPSCHITZIAN AND Φ-STRONGLY PSEUDOCONTRACTIVE MAPPINGS
Zhiqun Xue · Bulletin of the Korean Mathematical Society · 2008
In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and $\Phi$ -strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].