Strong convergence of approximated iterations for asymptoticallypseudocontractive mappings
Yonghong Yao, Mihai Postolache, Shin Min Kang · Fixed Point Theory and Applications · 2014
Abstract The asymptotically nonexpansive mappings have been introduced by Goebel and Kirkin 1972. Since then, a large number of authors have studied the weak and strongconvergence problems of the iterative algorithms for such a class of mappings.It is well known that the asymptotically nonexpansive mappings is a propersubclass of the class of asymptotically pseudocontractive mappings. In thepresent paper, we devote our study to the iterative algorithms for finding thefixed points of asymptotically pseudocontractive mappings in Hilbert spaces. Wesuggest an iterative algorithm and prove that it converges strongly to the fixedpoints of asymptotically pseudocontractive mappings. MSC: 47J25, 47H09, 65J15.