Existence of Fixed Points of Firmly Nonexpansive-Like Mappings in Banach Spaces
نویسندگان
چکیده
منابع مشابه
On fixed points of fundamentally nonexpansive mappings in Banach spaces
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...
متن کاملon fixed points of fundamentally nonexpansive mappings in banach spaces
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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We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...
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Let C be a subset of a Banach space E. A mapping T : C → E is nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖ for all x, y ∈ C. In 1965, it was proved independently by Browder 1 , Göhde 2 , and Kirk 3 that if C is a bounded closed convex subset of a Hilbert space and T : C → C is nonexpansive, then T has a fixed point. Combining the results above, Ray 4 obtained the following interesting result see 5 for a...
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ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2010
ISSN: 1687-1812
DOI: 10.1155/2010/512751