Effective metastability for modified Halpern iterations in CAT(0) spaces
نویسندگان
چکیده
منابع مشابه
Effective metastability for modified Halpern iterations in CAT(0) spaces
*Correspondence: kohlenbach@mathematik. tu-darmstadt.de Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstrasse 7, Darmstadt, 64289, Germany Abstract We examine convergence results for modified Halpern iterations due to Cuntavepanit and Panyanak (Fixed Point Theory Appl. 2011:869458, 2011). Following Kohlenbach and Leuştean (Adv. Math. 231:2525-2556, 2012), we extract ...
متن کاملEffective metastability of Halpern iterates in CAT(0) spaces
This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction of this rate from an ineffective proof due to Saejung is an instance of the general proof mining program which uses tools from mathematical logic to uncover hidden computational content from proofs. This me...
متن کاملStrong convergence and control condition of modified Halpern iterations in Banach spaces
Let C be a nonempty closed convex subset of a real Banach space X which has a uniformly Gâteaux differentiable norm. Let T ∈ ΓC and f ∈ΠC. Assume that {xt} converges strongly to a fixed point z of T as t→ 0, where xt is the unique element of C which satisfies xt = t f (xt) + (1− t)Txt. Let {αn} and {βn} be two real sequences in (0,1) which satisfy the following conditions: (C1) limn→∞αn = 0; (C...
متن کاملStrong convergence of Halpern iterations for quasi-nonexpansive mappings and accretive operators in Banach spaces
In this paper, we first introduce a new Halpern-type iterative scheme to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings in a uniformly convex Banach space. We then apply our method to approximate zeros of an infinite family of accretive operators and derive a st...
متن کاملRates of Asymptotic Regularity for Halpern Iterations of Nonexpansive Mappings
In this paper we obtain new effective results on the Halpern iterations of nonexpansive mappings using methods from mathematical logic or, more specifically, proof-theoretic techniques. We give effective rates of asymptotic regularity for the Halpern iterations of nonexpansive self-mappings of nonempty convex sets in normed spaces. The paper presents another case study in the project of proof m...
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: Fixed Point Theory and Applications
سال: 2012
ISSN: 1687-1812
DOI: 10.1186/1687-1812-2012-191