Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
نویسندگان
چکیده
منابع مشابه
Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
Let H be a real Hilbert space. Consider on H a nonexpansive semigroup S {T s : 0 ≤ s < ∞} with a common fixed point, a contraction f with the coefficient 0 < α < 1, and a strongly positive linear bounded self-adjoint operator A with the coefficient γ > 0. Let 0 < γ < γ/α. It is proved that the sequence {xn} generated by the iterative method x0 ∈ H, xn 1 αnγf xn βnxn 1 − βn I − αnA 1/sn ∫sn 0 T ...
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Let C be a closed convex subset of a Hilbert space H , let {T (t) : t ≥ 0}be a strongly continuous semigroup of non-expansive mapping on C such that ⋂ t≥0 F (T (t)) = ∅, and f : C → C be a fixed contractive mapping. Let {αn} and {tn} be sequences of real numbers satisfying 0 < αn < 1, tn > 0 and limn tn = limn αn tn = 0. Define a sequence {xn} in C by xn = αnf(xn) + (1 − αn)T (tn)xn, for n ∈ N....
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Copyright q 2011 Xue-song Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper is devoted to the strong convergence of two kinds of general viscosity iteration processes for approximating common fixed points of a n...
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This paper introduces an implicit scheme for a continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup. The main result is to prove the strong convergence of the proposed implicit scheme to the unique solutio...
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In this paper, we prove the following strong convergence theorem: Let C be a closed convex subset of a Hilbert space H. Let {T (t) : t ≥ 0} be a strongly continuous semigroup of nonexpansive mappings on C such that ⋂ t≥0 F ( T (t) ) 6= ∅. Let {αn} and {tn} be sequences of real numbers satisfying 0 < αn < 1, tn > 0 and limn tn = limn αn/tn = 0. Fix u ∈ C and define a sequence {un} in C by un = (...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2012
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2012/417234