New iterative schemes for a finite family of nonself uniformly quasi-Lipschitzian mappings in Banach spaces

New iterative schemes for a finite family of nonself uniformly quasi-Lipschitzian mappings in Banach spaces

* Correspondence: [email protected]. edu.cn School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, People’s Republic of China Full list of author information is available at the end of the article Abstract In this article, we introduce the concept of nonself uniformly quasi-Lipschitzian mapping and consider a new iterative scheme with errors to converge t...

Some Results for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces

Common fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

Iterative Schemes with Some Control Conditions for a Family of Finite Nonexpansive Mappings in Banach Spaces

The iterative schemes with some control conditions for a family of finite nonexpansive mappings are established in a Banach space. The main theorem improves results of Jung and Kim (also Bauschke). Our results also improve the corresponding results of Cho et al., Shioji and Takahashi, Xu, and Zhou et al. in certain Banach spaces and of Lions, O’Hara et al., and Wittmann in a framework of a Hilb...