Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space
نویسندگان
چکیده
منابع مشابه
Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space
with kn ≥ 0, rn ≥ 0, kn → 1, rn → 0 n → ∞ , for each x, y ∈ C, n 0, 1, 2, . . . . If kn 1 and rn 0, 1.1 reduces to nonexpansive mapping; if rn 0, 1.1 reduces to asymptotically nonexpansive mapping; if kn 1, 1.1 reduces to asymptotically nonexpansive-type mapping. So, a generalized asymptotically nonexpansive mapping is much more general than many other mappings. Browder 1 introduced the followi...
متن کاملStrong Convergence of an Implicit Iteration Process for Two Asymptotically Nonexpansive Mappings in Banach Spaces
The purpose of this paper is to introduce an implicit iteration process for approximating common fixed points of two asymptotically nonexpansive mappings and to prove strong convergence theorems in uniformly convex Banach spaces.
متن کاملStrong Convergence Theorem for Two Commutative Asymptotically Nonexpansive Mappings in Hilbert Space
where tn → 1 n → ∞ . We may assume that tn ≥ 1 for all n 1, 2, 3, . . . . Denote by F T the set of fixed points of T . Throughout this paper T and S : C → C are two commutative asymptotically nonexpansive mappings with asymptotical coefficients {tn} and {sn}, respectively. Suppose that F : F T ∩F S / ∅ 1, Goebel and Kirk’s theorem makes it possible . It is well known that F T and F S are convex...
متن کاملStrong Convergence of CQ Iteration for Asymptotically Nonexpansive Mappings
Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...
متن کاملConvergence and Stability of Modified Random SP-Iteration for A Generalized Asymptotically Quasi-Nonexpansive Mappings
The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2008
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2008/649510