[PDF] Top 20 Convergence theorems of common fixed points for some semigroups of nonexpansive mappings in complete CAT(0) spaces

... in CAT() spaces was first studied by Kirk [, ...every nonexpansive (single-valued) mapping defined on a bounded closed convex subset of a complete CAT() space always has a fixed ... See full document

... strong convergence theorems for countable families of asymptotically nonexpansive mappings and semigroups in Hilbert ...of nonexpansive mappings to asymptotically ... See full document

... existence theorems of fixed points, -convergence and strong convergence theorems for total asymptotically nonexpansive nonself mappings in the framework of ... See full document

... Very recently, Qin and Su 17 improved the result of Martinez-Yanes and Xu 10 from Hilbert spaces to Banach spaces. To be more precise, they proved the following theorem. Theorem QS. Let E be a uniformly ... See full document

... ≥ 0 whenever x tx − Qx ∈ C. A sunny nonexpansive retraction is a sunny retraction, which is also ...Sunny nonexpansive retractions play an important role in our ...sunny nonexpansive ... See full document

... complete CAT() space always has a fixed ...to CAT() spaces and proved that it is very similar to the weak conver- gence in the Banach space ...-convergence theorems for ... See full document

... 1. [[3], Proposition 2.4] Let K be a convex subset of X which is complete in the induced metric. Then for every x Î X, there exists a unique point P(x) Î K such that d(x, P(x)) = inf{d(x, y): y Î K}. Moreover, the ... See full document

... called nonexpansive (or a contractive) semigroup if l(s) = , for each s ∈ S, and asymptotically nonexpansive semigroup if lim s l(s) ≤ ...of common fixed points of ϕ, and by C a the set of ... See full document

... be nonexpansive if Tx − Ty ≤ x − y for each x, y ∈ ...of fixed points of ...constant 0 < α < 1 such that f x − fy ≤ αx − y for all x, y ∈ ...: 0 ≤ t < ∞} of mappings of ... See full document

... prove some convergence theorems for nonexpansive mappings in Banach ...in CAT(0) spaces for generalized nonexpansive mappings, which, in turn, ... See full document

... reversible semigroups of asymp- totically nonexpansive ...and convergence of fixed points for left amenable semigroups of asymptotically nonexpansive type mappings in ... See full document

... From the proof of Theorem 2.1, we give the following strong convergence theorem. Theorem 2.2. Let E be a real uniformly convex Banach space, let K be a nonempty closed convex subset of E, let T : K → K be a ... See full document

... semitopological semigroups include all commutative semigroups and all semitopological semigroups which are left amenable as discrete semigroups; see ... See full document

... Let (X, d) be a metric space. A geodesic path joining x Î X to y Î X (or, more briefly, a geodesic from x to y) is a map c from a closed interval [0, ℓ ] ⊆ R to X such that c (0) = x , c ( ℓ ) = y , and d ( ... See full document

... In , Kakavandi [] introduced the so-called half-space topology such that conver- gence in this topology is equivalent to -convergence for any sequence in a complete CAT() space. The author’s ... See full document

... any complete, simply connected Riemannian manifold having nonpositive sectional curvature is a CAT0 ...Pre-Hilbert spaces, R-trees see 1, Euclidean buildings see 2, the complex Hilbert ball with a ... See full document

... Development of this subject had been made by several authors [1,6-8]. The main purpose of this article is to extend this result of Rodé for a nonexpansive semigroup on a CAT(0) space in which the Δ ... See full document

... a complete CAT (0) space X ,t : K → K is a single-valued quasi-nonexpansive mapping and T : K → KC(K) is a mulivalued mapping satisfying conditions (E ) and (C λ ) for some λ ∈ ... See full document

... many convergence results by the proximal point algorithm (shortly, the PPA) which was initiated by Martinet [] in  for solving optimization problems have been extended from the classical linear spaces ... See full document

... c(t 0 )) = |t − t 0 | for t, t 0 ∈ [0, ...two points of X are joined by a geodesic and (ii) uniquely geodesic if there is exactly one geodesic joining x and y for each x, y ∈ X, which ... See full document