Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces
نویسندگان
چکیده
منابع مشابه
Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces
Let X be a real Banach space with a normalized duality mapping uniformly norm-to-weak continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping JΦ with gauge φ. Let f be an α-contraction and {Tn} a sequence of nonexpansive mapping, we study the strong convergence of explicit iterative schemes xn+1 = αnf(xn) + (1− αn)Tnxn (1) with a general theorem a...
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We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...
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* Correspondence: [email protected] Department of Mathematics, Ataturk University, Erzurum 25240, Turkey Full list of author information is available at the end of the article Abstract In this article, we first give a multivalued version of an iteration scheme of Agarwal et al. We use an idea due to Shahzad and Zegeye which removes a “strong condition” on the mapping involved in the ite...
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we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...
متن کاملIterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces
Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {Tk}k 1 : C → C an infinite family of nonexpansive mappings with the nonempty set of common fixed points ⋂∞ k 1 Fix Tk , and f : C → C a contraction. We introduce an explicit iterative algorithm xn 1 αnf xn 1 − αn Lnxn, where Ln ∑n k 1 ωk/sn Tk, Sn ∑n k 1 ωk, and wk > 0 with ∑∞ k 1 ωk 1. Under certain appropriat...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2008.11.041