... 1110. Xu, HK: Inequalities in Banach spaces with applications. Nonlinear Anal. 16, 1127–1138 (1991). doi:10.1016/0362-546X(91)90200-K11. Schu, J: Weakandstrongconvergence to fixed points of asymptotically ... strongconvergence theorem of an implicit-shrinking iterative processfor two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strongconvergence ... different from the strong convergence theorems for the implicit iterative processes in the literatures.Finally, we discuss a strongconvergence theorem concerning two nonexpansivemappings and the resolvent...
... quasinonexpansive mapping. However, the converse may be false [1, Example 2].Construction of approximating fixed points of nonlinear mappings is an importantsubject in the theory of nonlinear mappings and its ... cn=Lin et al. Fixed Point Theory and Applications 2011, 2011:96http://www.fixedpointtheoryandapplications.com/content/2011/1/96Page 14 of 2012. James, RC: Inner products in normed linear spaces. ... Banach space and let E* b e the dual space of E. For asequence {xn}ofE and a point x Î E, the weakconvergence of {xn}tox and the strong convergence of {xn}tox are denoted by xn⇀ x and xn®...
... 3502–3511,2009.8 M. O. Osilike and S. C. Aniagbosor, Weakandstrongconvergence theorems for fixed points ofasymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 32, no. 10, ... Xu, Weakandstrongconvergence theorems for strict pseudo-contractions in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 336–346, 2007.Fixed Point ... κ-strict pseudocontractions was introduced by Qihou 4 in 1996see also 5.KimandXu6 studied weakandstrongconvergence theorems for this classof mappings. It is important to note that...
... North-Holland, Amsterdam, The Netherlands, 2001.11 H. Iiduka and W. Takahashi, Strongconvergence theorems for nonexpansive mappings and inverse-strongly monotone mappings,” Nonlinear Analysis: ... and StrictPseudocontractions inHilbert Spaces Ming TianCollege of Science, Civil Aviation University of China, Tianjin 300300, ChinaCorrespondence should be addressed to Ming Tian, tianming1963@126.comReceived ... pseudocontraction mapping in thesetting of real Hilbert spaces. We proved strongconvergence theorems of the sequence generatedby our proposed schemes.1. IntroductionLet H be a real Hilbert space and C a...
... Combettes and S. A. Hirstoaga, “Equilibrium programming inHilbert spaces, ” Journal ofNonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005.24 W. Takahashi, Weakandstrongconvergence ... Methodfor 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 ... Wang, G. Marino, and F. H. Wang, Strongconvergence theorems for a generalized equilibriumproblem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a hilbert space,”...
... PseudocontractiveMappings inHilbert Spaces Xiaolong Qin,1Sun Young Cho,2 and Shin Min Kang31School of Mathematics and Information Sciences, North China University of Water Resources and Electric ... mappings. A weakconvergence theorem of fixed points is established in theframework of Hilbert spaces. 1. Introduction and PreliminariesThroughout this paper, we always assume that H is a real Hilbert ... pseudocontractions was introduced by Browder and Petryshyn 11 in areal Hilbert space. In 2007, Marino and Xu 12 obtained a weakconvergence theorem for theclass of strictly pseudocontractive mappings; see...
... nonexpansive mappings in Hilbert spaces. 2010 International Conference on Computational Intelligence and Software Engineering, CiSE 2010(2010). art. no. 56770647. Maingé, PE: Strongconvergence ... Access Strong convergent result for quasi-nonexpansivemappings inHilbert spaces Ming Tian* and Xin Jin* Correspondence:tianming1963@126.comCollege of Science, Civil AviationUniversity of China, ... nonexpan-sive mapping T. In 2009, Maingè [4] considered the viscosity approximation method (1.1), and expanded the strongconvergence to quasi-nonexpansive mappings inHilbert space. In 2010, Tian...
... and reproduction in any medium, provided the original work is properly cited.monotone mapping, T: K ® Hbel-inverse strongly monotone mapping. If g is anexpanding affine continuous mapping and ... I - F is an inverse strongly mono-tone mapping, and the fixed points set of mapping F and the solution set S(I - F)areequal. This means that our results contain the study of finding a common ... results and definitions.Definition2.1.LetA: H ® H be a mapping and K ⊂ H.Then,A is said to be semi-continuous at a point x in K iflimt→0A(x + th), y = A(x), y, x + th ∈ K, y ∈ H.Definition2.2....
... pagesdoi:10.1155/2010/547828Research Article Convergence of Paths for Perturbed MaximalMonotone Mappings inHilbert Spaces Yuan Qing,1Xiaolong Qin,1Haiyun Zhou,2 and Shin Min Kang31Department of Mathematics, ... RA to denote the domain and the range of the mapping A. → and denote strongandweak convergence, respectively.Recall the following well-known definitions.1 A mapping A : C → H is said ... T is said to behemicontinuous if it is continuous from each line segment in X to the weak topology in X∗.7 The mapping f with the domain Df and the range Rf in H is said to bepseudocontractive...
... 1.2 converges weakly to a point in FT.Therefore, many authors try to modify Mann’s iteration process to have strong convergence. In 2005, Kim and Xu 3 introduced the following iteration ... mapping Knis called the K-mapping generated by T1, ,TN and γn,1,γn,2, ,γn,N. In this paper, motivated by Kim and Xu 3,MarinoandXu10,Xu5, Yao et al. 4,andShang et al. 8, we introduce ... original work is properly cited.We introduce a new general iterative method by using the K-mapping for finding a common fixedpoint of a finite family of nonexpansive mappings in the framework of Hilbert...