... 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® ... Lin et al.: Weakandstrongconvergence theorems of implicit iteration process on Banachspaces. Fixed Point Theory and Applications 2011 2011:96.Submit your manuscript to a journal and benefi ... J: Weakandstrongconvergence to fixed points of asymptotically non-expansive mappings. Bull Austral MathSoc. 43, 153–159 (1991). doi:10.1017/S0004972700028884Lin et al. Fixed Point Theory and...
... 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® ... Lin et al.: Weakandstrongconvergence theorems of implicit iteration process on Banachspaces. Fixed Point Theory and Applications 2011 2011:96.Submit your manuscript to a journal and benefi ... two nonexpansive mappings and a relative nonexpansive mapping on Banachspaces. Note that the conditions of strongconvergence theorem are different from the strong convergence theorems for the...
... 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, ... 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 every ... 2007.11 G. Marino and H K. Xu, Weakandstrongconvergence theorems for strict pseudo-contractions inHilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1,...
... spaces, Fixed Point Theory and Appl., vol. 2010,Article ID 262691, 12 (2010)[20] Takahashi, W: Weakandstrongconvergence theorems for families of nonexpansivemappings and their applications. ... appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon. Strong convergence theorems and rate of convergence of multi-step iterativemethods for ... problems and fixed point problems with applications. Nonlinear Anal.72, 99–112 (2010)[18] Shimoji, K, Takahashi, W: Strongconvergence to common fixed points of infinitenonexpansive mappings and applications....
... al.: Strongconvergence of a hybrid method for monotone variational inequalities and fixed point problems. Fixed Point Theory and Applications 2011 2011:53.Submit your manuscript to a journal and ... {zn} converge weakly tothesameelementofNi=1Fix(Si) ∩if and only if lim infn〈Axn, x - xn〉 ≥ 0, ∀x Î C.Note that Ceng, Teboulle and Yao’s method has only weak convergence. Very ... approximation method are well defined and converge stronglyto PF(S)∩Ω.Moti vated and inspired by the works of Nadezhkina and Takaha shi [23], Ceng et al.[25], and Ceng et al. [27], in this paper...
... 1n0T(t)yndt, n ≥ 0.Then {xn} and {yn} convergence strongly to x* which is the unique solution of the sys-tems of variational inequalities:Piri and Badali Fixed Point Theory and Applications 2011, ... δn+1Bxn) .Piri and Badali Fixed Point Theory and Applications 2011, 2011:55http://www.fixedpointtheoryandapplications.com/content/2011/1/55Page 9 of 16RESEARC H Open Access Strong convergence ... ε-approximate fixed points ofT, i.e., Fε(T; D)={x Î D :||x - Tx|| ≤ ε }. Weakconvergence is denoted by ⇀ and strongconvergence is denoted by ®.3 Main resultsTheorem 3.1 Let S be a semigroup,...
... product 〈·,·〉 andnorm||·||,andletC be aclosed convex subset of H.Wewritexn⇀ x to indicate that the sequence {xn}con-verges weakly to x,andxn® x implies that {xn} converges strongly to ... article as: Bunyawat and Suantai: Strongconvergence theorems for variational inequalities and fixedpoints of a countable family of nonexpansive mappings. Fixed Point Theory and Applications 2011 ... q≤0.Bunyawat and Suantai Fixed Point Theory and Applications 2011, 2011:47http://www.fixedpointtheoryandapplications.com/content/2011/1/47Page 9 of 13Then, T is maximal monotone and 0 Î Tv if and only...
... and relatively nonexpansive mappings. Fixed Point Theory Appl 2008, 2008:11, (Article ID 528476).9. Takahashi W, Zembayashi K: Strongandweakconvergence theorems for equilibrium problems and ... PreliminariesLet E be a real Banach space, and {xn}beasequenceinE.Wedenotebyxn® x and xn⇀ x the strongconvergenceandweakconvergence of {xn}, respectively. The normal-ized duality mapping J : ... Θi(Θi> 0), and Fis bounded in C.Qu and Cheng Fixed Point Theory and Applications 2011, 2011:17http://www.fixedpointtheoryandapplications.com/content/2011/1/17Page 7 of 13 and common zero-point...
... is bounded, closed and con-vex and T is a nonexpansive mapping of C into itself, then F(T) is nonem pty; forinstance, see [5]. Recently, Tada and Takahashi [6] and Takahashi and Takahashi [7]considered ... Kangtunyakarn: Strongconvergence theorem for a generalized equilibrium problem and system of variational inequalities problem and infinite family of strict pseudo-contractions. Fixed Point Theory and Applications ... b < 1, and αj1, αj2, αj3∈ (κ,1)for all j = 1, 2, . For every n Î N, let Sn and S are S-mapping gener-ated by Tn, ,T1 and rn, rn-1, , r1 and Tn, Tn-1, , and rn, rn-1,...
... notations:1. ⇀ for the weakconvergenceand ® for the strong convergence. 2.ωw(xn)={x : ∃xnj x}denotes the weak ω-limit set of {xn}.2. PreliminariesWe need some facts and tools in a real ... (2009). doi:10.1016/j.na.2008.02.09014. Tada, A, Takahashi, W: Weakandstrongconvergence theorems for a nonexpansive mappingand a equilibriumproblem. J Optim Theory Appl. 133, 359–370 (2007). ... [0, 1/2] and C2: = (1/2, 1]. Hence,|Tnx − Tny| = kn|x −y|≤|x −y| for all x,y∈ C1 and n ∈N and |Tnx − Tny| =0≤|x −y| for all x,y∈ C2 and n ∈ N.For x Î C1 and y Î...
... 14 Fixed Point Theory and Applications19 W. Takahashi and Kei Zembayashi, Strongandweakconvergence theorems for equilibriumproblems and relatively nonexpansive mappings ... Accretive and Monotone Type,vol.178 of Lecture Notes in Pure and Applied Mathematics, pp. 15–50, Marcel Dekker, New York, NY, USA,1996.2 S Y. Matsushita and W. Takahashi, Weakandstrongconvergence ... 20–30, 2009.15 A. Tada and W. Takahashi, Weakandstrongconvergence theorems for a nonexpansive mapping and an equilibrium problem,” Journal of Optimization Theory and Applications, vol. 133,...
... Su and Qin 6 modified the hybrid iteration method of Nakajo and Takahashi through the monotone hybrid method, and to prove strongconvergence theorems.In 2008, Takahashi et al. 7 proved strong ... asymptoticallynonexpansive mappings and semigroups in a Hilbert space, and to prove strong convergence theorems. Our results presented are improvement and extension of the corresponding resultsin 3, 5–8 and many authors.2. ... 957–961, 1967.3 K. Nakajo and W. Takahashi, Strongconvergence theorems for nonexpansive mappings and nonexpansive semigroups,” Journal of Mathematical Analysis and Applications, vol. 279,...
... Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” Journal ofNonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005.24 W. Takahashi, Weakandstrongconvergence ... A. Moudafi, Weakconvergence theorems for nonexpansive mappings and equilibrium problems,”Journal of Nonlinear and Convex Analysis, vol. 9, no. 1, pp. 37–43, 2008.15 S. Plubtieng and R. Punpaeng, ... quasi-φ-nonexpansive mappings and equilibrium problems,” Journal of Computational and Applied Mathematics,vol. 234, no. 3, pp. 750–760, 2010.18 S. H. Wang, G. Marino, and F. H. Wang, Strongconvergence theorems...