The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multivalued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.

Let X be a real uniformly smooth Banach space and let T : D(T) ⊆ X → X be a K-positive definite operator. Under suitable conditions we establish that the iterative method by Bai (1999) converges strongly to the unique solution of the equation Tx = f , f ∈ X. The results presented in this paper generalize the corresponding results of Bai (1999), Chidume and Aneke (1993), and Chidume and Osilike ...

The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-φ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the p...

* Correspondence: [email protected] Department of Mathematics Education, Kyungnam University, Masan, Kyungnam, 631-701, Korea Full list of author information is available at the end of the article Abstract We study the strong convergence of a regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and unifo...

For an isometric action of a finitely generated group on the ultralimit of a sequence of global Busemann nonpositive curvature spaces, we state a sufficient condition for the existence of a fixed point of the action in terms of the energy of equivariant maps from the group into the space. Furthermore, we show that this energy condition holds for every isometric action of a finitely generated gr...

The purpose of this paper is to give a regularization method to obtain the strong convergence of iterative sequence to a solution of the problem of finding a common fixed point of a finite family nonexpansive mappings in an uniformly convex and uniformly smooth Banach space.