Strong convergence theorems by hybrid method for asymptotically [formula omitted]-strict pseudo-contractive mapping in Hilbert space

Abstract

In this paper, we introduce the hybrid method of modified Mann’s iteration for an asymptotically k -strict pseudo-contractive mapping. Then we prove that such a sequence converges strongly to P F ( T ) x 0 . This main theorem improves the result of Issara Inchan [I. Inchan, Strong convergence theorems of modified Mann iteration methods for asymptotically nonexpansive mappings in Hilbert spaces, Int. J. Math. Anal. 2 (23) (2008) 1135–1145] and concerns the result of Takahashi et al. [W. Takahashi, Y. Takeuchi, R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 341 (2008) 276–286], and many others.