Strong convergence theorems for a semigroup of nonexpansive mappings in Banach spaces
Само за регистроване кориснике
2010
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Let E be a real reflexive Banach space, which admits a weakly sequentially continuous duality mapping of E into E*, and C be a nonempty closed convex subset of E. Let {T (t) : t >= 0} be a semigroup of nonexpansive self-mappings on C such that F := boolean AND(t >= 0)Fix(T(t)) not equal empty set, where Fix(T(t)) = {x is an element of C: x = T(t)x}, and let f: C -> C be a fixed contractive mapping. If {alpha(n)}, {beta(n)}, {t(n)} satisfy some appropriate conditions, then a iterative process {x(n)} in C, defined by x(n) = alpha(n)y(n) + (1 - alpha(n))T(t(n))x(n), y(n) = beta(n)f(x(n-1)) + (1 - beta(n))x(n-1) converges strongly to q is an element of F, and q is the unique solution in F to the following variational inequality: LT (I - f)q, j(q - u)> LT = 0 for all u is an element of F. Our results extend and improve corresponding ones of Suzuki [T. Suzuki, On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131 (2002), pp. 2...133-2136.], Xu [H.K. Xu, A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72 (2005), pp. 371-379.] and Chen and He [R. D. Chen and H. He, Viscosity approximation of common fixed points of nonexpansive semigroups in Banach space, Appl. Math. Lett. 20 (2007), pp. 751-757.].
Кључне речи:
strong convergence / nonexpansive semigroups / impreflexive Banach space / fixed point / contraction mappingИзвор:
International Journal of Computer Mathematics, 2010, 87, 11, 2419-2425Издавач:
- Taylor & Francis Ltd, Abingdon
Финансирање / пројекти:
- National Science Foundation of China [10771050]
DOI: 10.1080/00207160902887515
ISSN: 0020-7160
WoS: 000281701200004
Scopus: 2-s2.0-77956555935
Институција/група
Fakultet organizacionih naukaTY - JOUR AU - Ćirić, Ljubomir B. AU - He, Huimin AU - Chen, Rudong AU - Lazović, Rade PY - 2010 UR - https://rfos.fon.bg.ac.rs/handle/123456789/655 AB - Let E be a real reflexive Banach space, which admits a weakly sequentially continuous duality mapping of E into E*, and C be a nonempty closed convex subset of E. Let {T (t) : t >= 0} be a semigroup of nonexpansive self-mappings on C such that F := boolean AND(t >= 0)Fix(T(t)) not equal empty set, where Fix(T(t)) = {x is an element of C: x = T(t)x}, and let f: C -> C be a fixed contractive mapping. If {alpha(n)}, {beta(n)}, {t(n)} satisfy some appropriate conditions, then a iterative process {x(n)} in C, defined by x(n) = alpha(n)y(n) + (1 - alpha(n))T(t(n))x(n), y(n) = beta(n)f(x(n-1)) + (1 - beta(n))x(n-1) converges strongly to q is an element of F, and q is the unique solution in F to the following variational inequality: LT (I - f)q, j(q - u)> LT = 0 for all u is an element of F. Our results extend and improve corresponding ones of Suzuki [T. Suzuki, On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131 (2002), pp. 2133-2136.], Xu [H.K. Xu, A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72 (2005), pp. 371-379.] and Chen and He [R. D. Chen and H. He, Viscosity approximation of common fixed points of nonexpansive semigroups in Banach space, Appl. Math. Lett. 20 (2007), pp. 751-757.]. PB - Taylor & Francis Ltd, Abingdon T2 - International Journal of Computer Mathematics T1 - Strong convergence theorems for a semigroup of nonexpansive mappings in Banach spaces EP - 2425 IS - 11 SP - 2419 VL - 87 DO - 10.1080/00207160902887515 UR - conv_1283 ER -
@article{ author = "Ćirić, Ljubomir B. and He, Huimin and Chen, Rudong and Lazović, Rade", year = "2010", abstract = "Let E be a real reflexive Banach space, which admits a weakly sequentially continuous duality mapping of E into E*, and C be a nonempty closed convex subset of E. Let {T (t) : t >= 0} be a semigroup of nonexpansive self-mappings on C such that F := boolean AND(t >= 0)Fix(T(t)) not equal empty set, where Fix(T(t)) = {x is an element of C: x = T(t)x}, and let f: C -> C be a fixed contractive mapping. If {alpha(n)}, {beta(n)}, {t(n)} satisfy some appropriate conditions, then a iterative process {x(n)} in C, defined by x(n) = alpha(n)y(n) + (1 - alpha(n))T(t(n))x(n), y(n) = beta(n)f(x(n-1)) + (1 - beta(n))x(n-1) converges strongly to q is an element of F, and q is the unique solution in F to the following variational inequality: LT (I - f)q, j(q - u)> LT = 0 for all u is an element of F. Our results extend and improve corresponding ones of Suzuki [T. Suzuki, On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131 (2002), pp. 2133-2136.], Xu [H.K. Xu, A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72 (2005), pp. 371-379.] and Chen and He [R. D. Chen and H. He, Viscosity approximation of common fixed points of nonexpansive semigroups in Banach space, Appl. Math. Lett. 20 (2007), pp. 751-757.].", publisher = "Taylor & Francis Ltd, Abingdon", journal = "International Journal of Computer Mathematics", title = "Strong convergence theorems for a semigroup of nonexpansive mappings in Banach spaces", pages = "2425-2419", number = "11", volume = "87", doi = "10.1080/00207160902887515", url = "conv_1283" }
Ćirić, L. B., He, H., Chen, R.,& Lazović, R.. (2010). Strong convergence theorems for a semigroup of nonexpansive mappings in Banach spaces. in International Journal of Computer Mathematics Taylor & Francis Ltd, Abingdon., 87(11), 2419-2425. https://doi.org/10.1080/00207160902887515 conv_1283
Ćirić LB, He H, Chen R, Lazović R. Strong convergence theorems for a semigroup of nonexpansive mappings in Banach spaces. in International Journal of Computer Mathematics. 2010;87(11):2419-2425. doi:10.1080/00207160902887515 conv_1283 .
Ćirić, Ljubomir B., He, Huimin, Chen, Rudong, Lazović, Rade, "Strong convergence theorems for a semigroup of nonexpansive mappings in Banach spaces" in International Journal of Computer Mathematics, 87, no. 11 (2010):2419-2425, https://doi.org/10.1080/00207160902887515 ., conv_1283 .