Approximation of fixed points of some classes of nonlinear mappings

We introduce a new class of nonlinear mappings, the class of generalized strongly successively Φ- hemicontractive mappings in the intermediate sense and prove the convergence of Mann type iterative scheme with errors to their fixed points. This class of nonlinear mappings is more general than those defined by several authors. In particular, the class of generalized strongly successively Φ- hemicontractive mappings in the intermediate sense introduced in this study is more general than the class defined by Liu et al. [Z. Liu, J. K. Kim and K. H. Kim, Convergence theorems and stability problems of the modified Ishikawa iterative sequences for strictly successively hemicontractive mappings, Bull. Korean Math. Soc. 39 (2002), No. 3, pp. 455-469].