Convergence to common fixed point of nonexpansive semigroups
نویسندگان
چکیده
منابع مشابه
On Strong Convergence to Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
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 = (...
متن کاملCommon Fixed Points of Commutative Semigroups of Nonexpansive Mappings
Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F (T ) the set of fixed points of T . Kirk [21] proved that F (T ) is nonempty in the case that C is weakly compact and has normal structure. See also [3, 4, 5, 14] and others. If C is weakly compact and E has the Opial property, then C has n...
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The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...
متن کاملNormal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces
A closed convex subset C of a Banach space E has normal structure if for each bounded closed convex subsetD of Cwhich contains more than one point, there is a point x ∈ D which is not a diametral point of D, that is, sup {‖x − y‖ : y ∈ D} < δ D , where δ D the diameter of D. The set C is said to have fixed point property FPP if every nonexpansive mapping T : C → C has a fixed point. In 1 , Kirk...
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This paper is concerned with a common fixed point problem of a nonexpansive semigroup in Hilbert spaces. The strong convergence theorem for a nonexpansive semigroup is obtained by a novel general iterative scheme based on the viscosity approximation method and applicability of the results is shown to extend the results of many authors existing in the current literature. Mathematics Subject Clas...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.01.009