Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings
نویسندگان
چکیده
منابع مشابه
Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings
Suppose that E is a real normed linear space, C is a nonempty convex subset of E, T : C → C is a Lipschitzian mapping, and x∗ ∈ C is a fixed point of T . For given x0 ∈ C, suppose that the sequence {xn} ⊂ C is the Mann iterative sequence defined by xn 1 1−αn xn αnTxn, n ≥ 0, where {αn} is a sequence in 0, 1 , ∑∞ n 0 α 2 n < ∞, ∑∞ n 0 αn ∞. We prove that the sequence {xn} strongly converges to x...
متن کاملA Sufficient and Necessary Condition for Halpern-type Strong Convergence to Fixed Points of Nonexpansive Mappings
In this paper, we prove a Halpern-type strong convergence theorem for nonexpansive mappings in a Banach space whose norm is uniformly Gâteaux differentiable. Also, we discuss the sufficient and necessary condition about this theorem. This is a partial answer of the problem raised by Reich in 1983.
متن کاملFixed-point Iteration Processes for Non-lipschitzian Mappings of Asymptotically Quasi-nonexpansive Type
We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...
متن کاملImplicit Mann fixed point iterations for pseudo-contractive mappings
Let K be a compact convex subset of a real Hilbert space H and T:K→K a continuous hemicontractive map. Let {an},{bn} and {cn} be real sequences in [0, 1] such that an+bn+cn=1, and {un} and {vn} be sequences in K. In this paper we prove that, if {bn}, {cn} and {vn} satisfy some appropriate conditions, then for arbitrary x0K, the sequence {xn} defined iteratively by xn=anxn−1+bnTvn+cnun;n≥1, conv...
متن کاملRemarks on Lipschitzian Mappings and Some Fixed Point Theorems
Let X, Y be the normed spaces, C ⊂ X a convex set, and T : C → Y a continuous mapping. Some weak conditions implying the Lipschitz continuity of T are presented. Applications to the fixed point theory and theory of composition operators are presented.
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: Journal of Applied Mathematics
سال: 2012
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2012/327878