weak and strong convergence theorems for strict pseudocontractions in hilbert spaces

Ngày tải lên: 22/06/2014, 06:20

Ngày tải lên: 23/06/2014, 00:20

... iteration and the modified Ishikawa iteration, Zhou 3 obtained some weak and strong convergence theorems for λ -strict pseudocontractions in Hilbert spaces which extend the corresponding results in ... pages doi:10.1155/2010/150539 Research Article Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces Liang-Gen Hu, 1 Wei-Wei Lin, 2 and Jin-Ping Wang 1 1 Department of Mathematics, Ningbo University, ... Mathematical Analysis and Applications, vol. 20, pp. 197–228, 1967. 2 G. Marino and H K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, ” Journal of...

Ngày tải lên: 21/06/2014, 11:20

... asymptotically κ -strict pseudocontractions was introduced by Qihou 4 in 1996 see also 5.KimandXu6 studied weak and strong convergence theorems for this class of mappings. It is important ... Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 336–346, 2007. Fixed Point ... 3502–3511, 2009. 8 M. O. Osilike and S. C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 32, no. 10,...

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Ngày tải lên: 23/06/2014, 00:20

... different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem concerning two nonexpansive mappings and the resolvent ... strong convergence theorem of an implicit-shrinking iterative process for two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strong convergence ... point sets of nonexpansive mappings in Banach spaces. Trans Am Math Soc. 179, 251–262 (1973) 17. Browder, FE: Fixed point theorems for noncompact mappings in Hilbert spaces. Proc Nat Acad Sci USA....

Ngày tải lên: 20/06/2014, 21:20

... point sets of nonexpansive mappings in Banach spaces. Trans Am Math Soc. 179, 251–262 (1973) 17. Browder, FE: Fixed point theorems for noncompact mappings in Hilbert spaces. Proc Nat Acad Sci USA. ... Banach space and let E* b e the dual space of E. For a sequence {x n }ofE and a point x ẻ E, the weak convergence of {x n }tox and the strong convergence of {x n }tox are denoted by x n x and x n đ ... values in I.) And they proved the weak convergence of p ro- cess (1.3) to a common fixed point in the setting of a Hilbert space. In 2010, K han et al. [5] presented an implicit iterative process for...

Ngày tải lên: 20/06/2014, 21:20

... convergence theorems for nonexpansive mappings in Banach spaces. J Math Anal Appl. 67, 274–276 (1979). doi:10.1016/0022-247X(79)90024-6 10. Suzuki, T: Strong convergence theorems for infinite families ... λ n A ) x n − p ) → 0 . □ We now obtain the fo llowing weak conv ergence theorems in uniforml y convex spaces. Theorem 3.13. Let E be a uniformly convex and 2-uniformly smooth Banach space. Let C ... J(Qx-y) 0forallx ẻ E and y ẻ C. In this case, Q is uniquely determined. Using this result, Aoya ma et al. obtained the following result. Recall that, for a mapping T : C đ E,the set of fixed points...

Ngày tải lên: 21/06/2014, 01:20

... North-Holland, Amsterdam, The Netherlands, 2001. 11 H. Iiduka and W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse- strongly monotone mappings,” Nonlinear Analysis: ... 43–52, 2006. 7 X. Qin, M. Shang, and S. M. Kang, Strong convergence theorems of modified Mann iterative process for strict pseudo-contractions in Hilbert spaces, ” Nonlinear Analysis: Theory, ... method for finding an element of EPφ ∩ FS,whereS : C → H is a k-strictly pseudocontractive non-self mapping, and then obtained two strong convergence theorems. Journal of Inequalities and Applications...

Ngày tải lên: 21/06/2014, 05:20

... Duan and Zhao: Strong convergence theorems for system of equilibrium problems and asymptotically strict pseudocontractions in the intermediate sense. Fixed Point Theory and Applications 2011 2011:13. Submit ... Hu and Cai [3] further considered the asymptotically strict pseudocon- tractive mappings in the intermediate sense concerning equilibrium problem. They obtained the following result in a real Hilbert ... LetCbeanonemptyclosedconvexsubsetofarealHilbertspaceH and N ≥ 1 be an integer, j : C đ C be a bifunction satisfying (A1)-(A4) and A : C đ Hbeana-inverse-strongly monotone mapping. Let for each 1 ≤ i ≤ N, T i : C ® Cbea uniformly...

Ngày tải lên: 21/06/2014, 02:20

... converge in a Hilbert space; see 4. In 1967, Browder-Petryshyn 2 introduced the class of strict pseudocontractions and proved existence and weak convergence theorems in a real Hilbert setting ... of Mathematical Analysis and Applications, vol. 67, no. 2, pp. 274–276, 1979. 7 G. Marino and H K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, ” Journal ... Q. H. Ansari, and J. C. Yao, Strong and weak convergence theorems for asymptotically strict pseudocontractive mappings in intermediate sense,” Journal of Nonlinear and Convex Analysis, vol. 11,...

Ngày tải lên: 21/06/2014, 11:20

... obtain strong convergence theorems for a countable family of nonexpansive mappings and a strictly pseudocontractive mapping, and a countable family of uniformly k-strictly pseudocontractive mappings ... Iterative algorithms for nonlinear operators. J Lond Math Soc. 2, 240–256 (2002) 9. Zhou, H: Convergence theorems of fixed points for k -strict pseudo-contractions in Hilbert spaces. Nonlinear Anal. 69, 456–462 ... article as: Bunyawat and Suantai: Strong convergence theorems for variational inequalities and fixed points of a countable family of nonexpansive mappings. Fixed Point Theory and Applications 2011...

Ngày tải lên: 21/06/2014, 00:20

... subset of H and T : K đ H be a mapping. In this paper, the set of fixed points of T is denoted by F(T). We use symbols đ and to denote strong and weak convergence, respectively. For each point x ẻ ... problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Under appropriate conditions, some strong convergence theorems are established. The results obtained in this ... Studies in Advanced Mathematics, vol. 28, Cambridge University Press, Cambridge (1990) 13. Suzuki, T: Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces. ...

Ngày tải lên: 21/06/2014, 01:20

... mappings were investigated in 20 .In 23 the weak convergence of three- step Noor iterative scheme for an I-nonexpansive mapping in a Banach space has been established. Recently, in 24 the weak ... no. 1, pp. 153–159, 1991. 13 N. Shioji and W. Takahashi, Strong convergence theorems for asymptotically nonexpansive semigroups in Hilbert spaces, ” Nonlinear Analysis: Theory, Methods & Applications, ... process for a finite family of nonexpansive mappings in Banach spaces, ” Fixed Point Theory and Applications, vol. 2006, Article ID 82738, 11 pages, 2006. 18 H. Y. Li and H. Z. Li, Strong convergence...

Ngày tải lên: 21/06/2014, 20:20

... CAT0 space always has a fixed point. Since then the fixed point theory for single-valued and multivalued mappings in CAT0 spaces has been rapidly developed and many of papers have appeared ... “Fixed point theorems in CAT0 spaces and R-trees,” Fixed Point Theory and Applications, vol. 2004, no. 4, pp. 309–316, 2004. 16 S. Dhompongsa, A. Kaewkhao, and B. Panyanak, “Lim’s theorems for ... regularity for CAT0 -spaces, ” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 386–399, 2007. 22 N. Shahzad and J. Markin, “Invariant approximations for commuting mappings in...

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Ngày tải lên: 22/06/2014, 19:20

Ngày tải lên: 22/06/2014, 22:20

... Method for In nite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces Shenghua Wang 1, 2 and Baohua Guo 1, 2 1 National Engineering Laboratory for ... and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces, ” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005. 24 W. Takahashi, Weak and strong convergence theorems ... Wang, G. Marino, and F. H. Wang, Strong convergence theorems for a generalized equilibrium problem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a hilbert space,”...

Ngày tải lên: 21/06/2014, 11:20

... Anthony To Ming Lau We introduce a modified Ishikawa iterative process for approximating a fixed point of two in nitely nonexpansive self-mappings by using the hybrid method in a Hilbert space and prove that ... P C n ∩Q n  x q  ,n≥ q 1.3 and prove, {x n } converges strongly to a fixed point of {T 1 n } and {T 2 n }. We will use the notation:  for weak convergence and → for strong convergence. ω w x n {x ... In nitely Nonexpansive Mappings in Hilbert Space Yi-An Chen College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China Correspondence should be...

Ngày tải lên: 21/06/2014, 20:20

... Takahashi, Y. Takeuchi, and R. Kubota, Strong convergence theorems by hybrid methods for fam- ilies of nonexpansive mappings in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol. ... recently proved a strong convergence theorem for nonexpansive semigroups in Hilbert spaces by hy- brid method in the mathematical programming. However, their proof of the main result 3, Theorem ... Takahashi, Strong convergence theorems for nonexpansive mappings and non- expansive semigroups,” Journal of Mathematical Analysis and Applications, vol. 279, no. 2, pp. 372–379, 2003. 3 H. He and...

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