The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

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The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi-φ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergen...

* Correspondence: ooly61@yahoo. co.kr; [email protected] Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea Full list of author information is available at the end of the article Abstract In this article, strong convergence of Krasnoselski-Mann iterative s...

In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth and strictly co...

In this paper, we define and study convergence of an Ishikawa type iteration scheme with a new and weaker control condition for two nonself asymptotically quasi-nonexpansive mappings on a uniformly convex Banach space.