... iteration and the modified Ishikawa iteration, Zhou 3obtained some weakandstrongconvergencetheoremsfor λ -strict pseudocontractions in Hilbertspaces which extend the corresponding results in ... pagesdoi:10.1155/2010/150539Research Article Strong ConvergenceTheoremsfor Strict Pseudocontractionsin Uniformly ConvexBanach Spaces Liang-Gen Hu,1Wei-Wei Lin,2 and Jin-Ping Wang11Department of Mathematics, Ningbo University, ... Mathematical Analysis and Applications, vol. 20, pp. 197–228, 1967.2 G. Marino and H K. Xu, Weakandstrongconvergencetheoremsforstrict pseudo-contractions in Hilbert spaces, ” Journal of...
... asymptotically κ -strict pseudocontractions was introduced by Qihou 4 in 1996see also 5.KimandXu6 studied weakandstrongconvergencetheoremsfor this classof mappings. It is important ... Xu, Weakandstrongconvergencetheoremsforstrict 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, Weakandstrongconvergencetheoremsfor fixed points ofasymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 32, no. 10,...
... different from the strong convergencetheoremsfor the implicit iterative processes in the literatures.Finally, we discuss a strongconvergence theorem concerning two nonexpansivemappings and the resolvent ... strongconvergence theorem of an implicit-shrinking iterative process for two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strongconvergence ... point sets of nonexpansive mappings in Banach spaces. Trans Am Math Soc. 179, 251–262(1973)17. Browder, FE: Fixed point theoremsfor noncompact mappings inHilbert spaces. Proc Nat Acad Sci USA....
... point sets of nonexpansive mappings in Banach spaces. Trans Am Math Soc. 179, 251–262(1973)17. Browder, FE: Fixed point theoremsfor noncompact mappings inHilbert spaces. Proc Nat Acad Sci USA. ... Banach space and let E* b e the dual space of E. For asequence {xn}ofE and a point x ẻ E, the weakconvergence of {xn}tox and the strong convergence of {xn}tox are denoted by xn x and xnđ ... values in I.) And they proved the weakconvergence 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...
... convergencetheoremsfor nonexpansive mappings in Banach spaces. J Math Anal Appl. 67, 274–276(1979). doi:10.1016/0022-247X(79)90024-610. Suzuki, T: Strongconvergencetheoremsfor infinite families ... λnA)xn− p)→ 0.□We now obtain the fo llowing weak conv ergence theoremsin 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,theset of fixed points...
... North-Holland, Amsterdam, The Netherlands, 2001.11 H. Iiduka and W. Takahashi, Strongconvergencetheoremsfor nonexpansive mappings and inverse-strongly monotone mappings,” Nonlinear Analysis: ... 43–52, 2006.7 X. Qin, M. Shang, and S. M. Kang, Strongconvergencetheorems of modified Mann iterative process for strict pseudo-contractions inHilbert spaces, ” Nonlinear Analysis: Theory, ... method for finding an element of EPφ ∩ FS,whereS : C → H isa k-strictly pseudocontractive non-self mapping, and then obtained two strong convergence theorems. Journal of Inequalities and Applications...
... Duan and Zhao: Strongconvergencetheoremsfor system of equilibrium problems and asymptotically strictpseudocontractionsin the intermediate sense. Fixed Point Theory and Applications 20112011:13.Submit ... Hu and Cai [3] further considered the asymptotically strict pseudocon-tractive mappings in the intermediate sense concerning equilibrium problem. Theyobtained 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 đHbeana-inverse-strongly monotone mapping. Let for each 1 ≤ i ≤ N, Ti: C ® Cbeauniformly...
... converge in a Hilbert space; see 4. In 1967, Browder-Petryshyn 2 introduced the class of strictpseudocontractions and proved existence andweakconvergencetheoremsin a real Hilbert setting ... ofMathematical Analysis and Applications, vol. 67, no. 2, pp. 274–276, 1979.7 G. Marino and H K. Xu, Weakandstrongconvergencetheoremsforstrict pseudo-contractions in Hilbert spaces, ” Journal ... Q. H. Ansari, and J. C. Yao, Strongandweakconvergencetheoremsfor asymptotically strict pseudocontractive mappings in intermediate sense,” Journal of Nonlinear and Convex Analysis,vol. 11,...
... obtain strongconvergencetheoremsfor a countable family ofnonexpansive mappings and a strictly pseudocontractive mapping, and a countablefamily of uniformly k-strictly pseudocontractive mappings ... Iterative algorithms for nonlinear operators. J Lond Math Soc. 2, 240–256 (2002)9. Zhou, H: Convergencetheorems of fixed points for k -strict pseudo-contractions inHilbert spaces. Nonlinear Anal. 69,456–462 ... article as: Bunyawat and Suantai: Strongconvergencetheoremsfor variational inequalities and fixedpoints of a countable family of nonexpansive mappings. Fixed Point Theory and Applications 2011...
... 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 strongandweak convergence, respectively. For each point x ẻ ... problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Underappropriate conditions, some strongconvergencetheorems are established. Theresults obtained in this ... Studies in Advanced Mathematics, vol. 28,Cambridge University Press, Cambridge (1990)13. Suzuki, T: Strongconvergencetheoremsfor infinite families of nonexpansive mappings in general Banach spaces. ...
... mappings were investigated in 20 .In 23 the weakconvergence of three-step Noor iterative scheme for an I-nonexpansive mapping in a Banach space has beenestablished. Recently, in 24 the weak ... no. 1, pp. 153–159, 1991.13 N. Shioji and W. Takahashi, Strongconvergencetheoremsfor asymptotically nonexpansivesemigroups inHilbert spaces, ” Nonlinear Analysis: Theory, Methods & Applications, ... process for a finite family of nonexpansivemappings 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...
... CAT0 space always has a fixed point. Since then the fixedpoint theory for single-valued and multivalued mappings in CAT0 spaces has been rapidlydeveloped and many of papers have appeared ... “Fixed point theoremsin CAT0 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 theoremsfor ... regularity for CAT0 -spaces, ” Journal of MathematicalAnalysis and Applications, vol. 325, no. 1, pp. 386–399, 2007.22 N. Shahzad and J. Markin, “Invariant approximations for commuting mappings in...
... Method for In nite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces Shenghua Wang1, 2 and Baohua Guo1, 21National Engineering Laboratory for ... and S. A. Hirstoaga, “Equilibrium programming inHilbert spaces, ” Journal ofNonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005.24 W. Takahashi, Weakandstrongconvergencetheorems ... Wang, G. Marino, and F. H. Wang, Strongconvergencetheoremsfor a generalized equilibriumproblem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a hilbert space,”...
... Anthony To Ming LauWe 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 provethat ... PCn∩Qnxq,n≥ q1.3 and prove, {xn} converges strongly to a fixed point of {T1n} and {T2n}.We will use the notation: forweakconvergenceand → forstrong convergence. ωwxn{x ... In nitelyNonexpansive Mappings inHilbert SpaceYi-An ChenCollege of Mathematics and Statistics, Chongqing Technology and Business University,Chongqing 400067, ChinaCorrespondence should be...
... Takahashi, Y. Takeuchi, and R. Kubota, Strongconvergencetheorems by hybrid methods for fam-ilies of nonexpansive mappings inHilbert spaces, ” Journal of Mathematical Analysis and Applications,vol. ... recentlyproved a strongconvergence theorem for nonexpansive semigroups inHilbertspaces by hy-brid method in the mathematical programming. However, their proof of the main result 3,Theorem ... Takahashi, Strongconvergencetheoremsfor nonexpansive mappings and non-expansive semigroups,” Journal of Mathematical Analysis and Applications, vol. 279, no. 2, pp. 372–379,2003.3 H. He and...