Bancha Panyanak

Demiclosed Principle for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

We prove the demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces. As a consequence, we obtain a -convergence theorem of the Krasnoselskii-Mann iteration for asymptotically nonexpansive mappings in this setting. Our results extend and improve many results in the literature.

Strong and Convergence Theorems for Multivalued Mappings in Spaces

We show strong and Open image in new window convergence for Mann iteration of a multivalued nonexpansive mapping whose domain is a nonempty closed convex subset of a CAT(0) space. The results we obtain are analogs of Banach space results by Song and Wang [2009, 2008]. Strong convergence of Ishikawa iteration are also included.We show strong and convergence for Mann iteration of a multivalued nonexpansive mapping whose domain is a nonempty closed convex subset of a CAT(0) space. The results we obtain are analogs of Banach space results by Song and Wang [2009, 2008]. Strong convergence of Ishikawa iteration are also included.

On the Ishikawa iteration processes for multivalued mappings in some CAT(κ) spaces

The purpose of this paper is to prove the strong convergence of the Ishikawa iteration processes for some generalized multivalued nonexpansive mappings in the framework of CAT(1) spaces. Our results extend the corresponding results given by Shahzad and Zegeye (Nonlinear Anal. 71:838-844, 2009), Puttasontiphot (Appl. Math. Sci. 4:3005-3018, 2010), Song and Cho (Bull. Korean Math. Soc. 48:575-584, 2011) and many others.

Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces

Abkar and Eslamian (Nonlinear Anal. TMA, 74, 1835-1840, 2011) prove that if K is a nonempty bounded closed convex subset of a complete CAT(0) space X, t : K → K is a single-valued quasi-nonexpansive mapping and T : K → KC(K) is a multivalued mapping satisfying conditions (E) and (Cλ) for some λ ∈ (0, 1) such that t and T commute weakly, then there exists a point z ∈ K such that z = t(z) ∈ T(z). In this paper, we extend this result to the general setting of uniformly convex metric spaces. Nevertheless, condition (E) of T can be weakened to the strongly demiclosedness of I - T.

Fixed Points for Multivalued Mappings in Uniformly Convex Metric Spaces

The purpose of this paper is to ensure the existence of fixed points for multivalued nonexpansive weakly inward nonself-mappings in uniformly convex metric spaces. This extends a result of Lim (1980) in Banach spaces. All results of Dhompongsa et al. (2005) and Chaoha and Phon-on (2006) are also extended.

On total asymptotically nonexpansive mappings in CAT(κ) spaces

In this article, we obtain the demiclosed principle, fixed point theorems and convergence theorems for the class of total asymptotically nonexpansive mappings on CAT(κ) spaces with κ>0. Our results generalize the results of Chang et al. (Appl. Math. Comput. 219:2611-2617, 2012), Tang et al. (Abstr. Appl. Anal. 2012:965751, 2012), Karapınar et al. (J. Appl. Math. 2014:738150, 2014) and many others.

Strong Convergence of Modified Halpern Iterations in CAT(0) Spaces

Strong convergence theorems are established for the modified Halpern iterations of nonexpansive mappings in CAT(0) spaces. Our results extend and improve the recent ones announced by Kim and Xu (2005), Hu (2008), Song and Chen (2008), Saejung (2010), and many others.

Generalized hybrid mappings on CAT(κ) spaces

In this paper, we obtain the demiclosed principle, fixed point theorems, and Δ-convergence theorems for the class of generalized hybrid mappings on CAT(κ) spaces with κ>0. Our results extend the results of Lin et al. (Fixed Point Theory Appl. 2011:49, 2011) and many others.

An approximation method for common fixed points of a finite family of asymptotic pointwise nonexpansive mappings

In this article, we consider an iterative scheme to approximate a common fixed point for a finite family of asymptotic pointwise nonexpansive mappings. We obtain weak and strong convergence theorems of the proposed iteration in uniformly convex Banach spaces. The related results for complete CAT(0) spaces are also included.MSC:47H09, 47H10.