The study of fixed points for multivalued contractions and nonexpansive maps using the Hausdorff metric was initiated by Markin [17]. Later, an interesting and rich fixed point theory for such maps has been developed. The theory of multivalued maps has applications in control theory, convex optimization, differential inclusions, and economics (see, e.g., [3, 8, 16, 22]). The theory of multivalu...

In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.

and Applied Analysis 3 problems for two countable families of quasi-φ-nonexpansive mappings and the common solution of variational inequality problems for a finite family of monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by the conditions. The results obtained in this paper extend an...

We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappi...

The purpose of this paper is to introduce a new hybrid projection method based on modified Mann iterative scheme by the generalized f-projection operator for a countable family of relatively quasi-nonexpansive mappings and the solutions of the system of generalized mixed equilibrium problems. Furthermore, we prove the strong convergence theorem for a countable family of relatively quasi-nonexpa...

In this paper, strong convergence theorems of Ishikawa type implicit iteration process with errors for a finite family of asymptotically nonexpansive in the intermediate sense and asymptotically quasi-pseudocontractive type mappings in normed linear spaces are established by using a new analytical method, which essentially improve and extend some recent results obtained by Yang [Convergence the...

In this paper, we consider the strong convergence of the projection type Ishikawa iteration process to a common fixed point of a finite family of nonself Ii asymptotically quasi-nonexpansive mappings. Our results of this paper improve and extend the corresponding results of Temir and Gul [10], Temir [11], and Thianwan [12].

In this paper, we consider the weak and strong convergence of implicit iteration process to a common fixed point of a finite family of nonself Ii-asymptotically quasi-nonexpansive mappings. Our results of this paper improve and extend the corresponding results of Shazad [8], Temir [5] and Gul [J. Math. Anal. Appl. 329(2007), 759-765]. Mathematics Subject Classification: 47H09, 47J25

*Correspondence: [email protected] 1Department of Mathematics, Hebei North University, Zhangjiakou, 075000, China Full list of author information is available at the end of the article Abstract The purpose of this article is to establish a kind of non-convex hybrid iteration algorithms and to prove relevant strong convergence theorems of common fixed points for a uniformly closed asymptotica...

In this paper, we propose a self-adaptive algorithm for solving the split common null point problem and fixed multivalued Bregman quasi-nonexpansive mappings in Banach spaces. We prove that sequence generated by our iterative scheme converges strongly to solution of above-mentioned problems under some suitable conditions. also apply main result feasibility Finally, numerical examples are given ...