In this paper, we show strong convergence theorems of modified Ishikawa iteration with errors and modified Halpern iteration with error for relatively nonexpansive mappings in a Banach space. The results extend and improve the corresponding results of Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others. Mathematics Subject Classification: 47H09; 47H10

The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve ...

We introduce a new modified Halpern-type iteration for a family of Bregman relatively nonexpansive mappings and establish strong convergence theorems in reflexive Banach spaces. The results extend the corresponding results obtained by many authors. Mathematics Subject Classification: 47H09; 47H10

The purpose of this paper is to introduce a modified Halpern-type iteration algorithm and prove strong convergence of the algorithm for quasi-φ-asymptotically non-expansive mappings. Our results improve and extend the corresponding results announced by many others.

In this paper, we introduce a new hybrid algorithm of modified Halpern iteration for a countable infinitely family of quasi-φ-nearly asymptotically nonexpansive mappings in Banach spaces and prove the strong convergence for the proposed algorithm. Our proof method is of novelty and the results presented in this paper improve the corresponding ones announced by others. Mathematics Subject Classi...

In this paper, we prove the strong convergence of the composite Halpern-type iteration for a family of nonexpansive mappings in CAT(0) spaces and compare our results with several recent results in this subject. Also, the inexact version of the Halpern iteration is studied in CAT(0) spaces.