[PDF] Top 20 An Implicit Algorithm for a Family of Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces

... A geodesic path joining x ∈ X to y ∈ X (or, more briefly, a geodesic from x to y) is a mapping c from a closed interval [0, l] ⊂ R to X such that c(0) = x, c(l) = y, and let d(c(t), c(t 0 )) = |t − t ... See full document

... the algorithm 1.6 to a common fixed point of a finite family of uniformly L-Lipschitzian and generalized asymptotically quasi-nonexpansive selfmaps in the general class of CAT0 ... See full document

... These show that the problem (1.1) is very general in the sense that numerous pro- blems in physics, optimization, and economics reduce to finding a solution of (1.1). Recently, some methods have been proposed for the ... See full document

... of nonexpansive mappings is Browder’s demiclosed principle [] which states that if X is a uniformly convex Banach space, C is a nonempty closed convex subset of X, and T : C → X is a nonexpansive ... See full document

... (generalized) asymptotically nonexpansive is closely related to the theory of fixed points in Banach spaces, and the implicit midpoint rule is one of the powerful numerical methods for solving ... See full document

... for asymptotically nonexpansive mappings and gave the ∆-convergence theorem of the modified Mann iteration process for above mentioned mappings in a CAT(0) ...in ... See full document

... hyperbolic spaces include several types of spaces including those of uniformly convex Banach spaces as well as CAT(0) ...Banach spaces as well as CAT(0) ... See full document

... an algorithm for solving the split feasibility problems for total quasi-asymptotically nonexpansive mappings in infinite-dimensional Hilbert ... See full document

... generalization by iterative methods has been of increasing research interest for numerous mathematicians in recent years. One of the first results of this nature was obtained by Browder [5] for nonexpansive self ... See full document

... of implicit Mann iteration processes with bounded perturbations for approximating a common fixed point of nonexpansive semigroup in CAT(0) ...of implicit Mann iteration schemes with ... See full document

... years, CAT() spaces have attracted the attention of many authors as they have played a very important role in different aspects of geometry ...a nonexpansive mapping defined on a bounded closed convex ... See full document

... 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 ... See full document

... A metric space X is a CAT() space if it is geodesically connected and if every geodesic triangle in X is at least as ‘thin’ as its comparison triangle in the Euclidean plane. That is to say, let (X, d) be a ... See full document

... for nonexpansive mappings in the setting of CAT() space have been studied extensively by many authors (see, for example, ...for asymptotically nonexpan- sive mappings in CAT() ... See full document

... Pre-Hilbert spaces, R-trees see 1, Euclidean buildings see 2, the complex Hilbert ball with a hyperbolic metric see 3, and many ...these spaces and of the fundamental role they play in geometry see Bridson ... See full document

... Iteration (3.1) has been considered in [2, 6, 7, 11, 12]. Iteration (3.1) has been dis- cussed in [1, 10]. Note that iteration (1.2) is a particular case of (3.1). However, as far as we know, no such paper is dedicated ... See full document

... of asymptotically nonexpansive mappings was introduced by Goebel and Kirk 1 in ...every asymptotically nonexpansive self-mapping T of C has a fixed ...of mappings see, ... See full document

... every nonexpansive mapping is asymptotically nonexpansive with the asymptotical sequence ...of asymptotically nonexpansive mappings was introduced by Goebel and Kirk 2 in ... See full document

... point algorithm using the S-type iteration process for two nonexpansive mappings in CAT() spaces and prove some convergence theorems of the proposed processes under some mild ... See full document

... generalized asymptotically nonexpansive mapping and gave a necessary and sufficient condition for the modi- fied Ishikawa and Mann iterative sequences to converge to fixed points for the class of ... See full document