Báo cáo hóa học: " Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications" pptx

... this 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 ... Thailand2Centre ofExcellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, ThailandAuthors’ contributionsAB study and researched nonlinear analysis and also wrote this article. SS participated ... inMathematics, CHE, Si AyutthayaRoad, Bangkok 10400, ThailandFull list of author information isavailable at the end of the articleAbstract A new general iterative method for finding a common element...

... pseudocontractions inHlibert spaces. Nonlinear Anal. 70, 1902–1911 (2009). doi:10.1016/j.na.2008.02.09014. Tada, A, Takahashi, W: Weak and strong convergence theorems for a nonexpansive mappingand a equilibrium problem. ... PCn∩Qn(u), for all n ∈ N,Duan and Zhao Fixed Point Theory and Applications 2011, 2011:13http://www.fixedpointtheoryandapplications.com/content/2011/1/13Page 3 of 13RESEA R C H Open Access Strong convergence ... + a }is convex (and closed).Duan and Zhao Fixed Point Theory and Applications 2011, 2011:13http://www.fixedpointtheoryandapplications.com/content/2011/1/13Page 4 of 13(4) S is asymptotically...

... 2400–2411.[8] K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonex-pansive semigroups, Journal of Mathematical Analysis and Applications 279 (2003), no. ... of accretive operators in Banach spaces,Journalof Mathematical Analysis and Applications 75 (1980), no. 1, 287–292.[11], Approximating fixed points of nonexpansive mappings, Panamerican Mathematical ... Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces,JournalofMathematical Analysis and Applications 67 (1979), no. 2, 274–276.[10], Strong conve rgence theorems for resolvents...

... (Ger-man).[10] B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc. 73 (1967), 957–961.[11] S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space,Proc.Amer.Math. ... using Lemma 2.1, we obtain the following useful lemma, which is a generalizationof [19, Lemma 2] and [20, Lemma 6].Lemma 2.2. Let {zn} and {wn} be bounded sequences in a Banach space E and let ... theorem for finite families of nonexpan-sive mappings in general Banach spaces. Motivated by Ishikawa’s result, we prove strong convergence theorems for infinite families of nonexpansive mappings.1....

... to an arbitrary interval and to the Ishikawa iteration and gave some control conditions for the convergence of Ishikawa iteration on an arbitrary in-terval. Recently, Phuengrattana and Suantai ... necessary and sufficient condition for the convergence ofIshikawa iteration on an arbitrary interval. J. Math. Anal. Appl. 323, 1383–1386(2006)[8] Atsushiba, S, Takahashi, W: Strong convergence theorems ... Kangtunyakarn and Suantai, we1This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon.Strong...

... (2006)doi:10.1186/1687-1812-2011-55Cite this article as: Piri and Badali: Strong convergence theorem for amenable semigroups of nonexpansivemappings and variational inequalities. Fixed Point Theory and Applications 2011 2011:55.Submit ... hand A x −Ay≤ A  x −y.Therefore,¯γ A 2 Ax − Ay2≤Ax − Ay, x − y.Piri and Badali Fixed Point Theory and Applications 2011, 2011:55http://www.fixedpointtheoryandapplications.com/content/2011/1/55Page ... doi:10.1016/j.na.2010.07.02714. Lau, AT, Miyake, H, Takahashi, W: Approximation of fixed points for amenable semigroups of nonexpansive mappings inBanach spaces. Nonlinear Anal. 67, 1211–1225 (2007). doi:10.1016/j.na.2006.07.00815....

... is nonem pty; for instance, see [5]. Recently, Tada and Takahashi [6] and Takahashi and Takahashi [7]considered iterative methods for finding an element of EP(G) ∩ F(T). Browder and Pet-ryshyn ... Nonlinear Functional Analysis. Yokohama Publishers, Yoko-hama (2000)6. Tada, A, Takahashi, W: Strong convergence theorem for an equilibrium problem and a nonexpansive mapping. J OptimTheory Appl. ... doi:10.1007/s10957-007-9187-z7. Takahashi, S, Takahashi, W: Viscosity approximation methods for equilibrium problems and fixed point problems inHilbert spaces. J Math Anal Appl. 331, 506–515 (2007). doi:10.1016/j.jmaa.2006.08.0368....

... conditions for the convergence of Ishikawa iteration on an arbitrary in-terval. Recently, Phuengrattana and Suantai [4] obtained a similar result for the new iteration, called the SP-iteration, and ... and Mann iterations for a class of Zamfirescu operators in arbitrary Banach spaces. Popescu [28] also used thisconcept to compare the rate of convergence of Picard and Mann iterations for a class ... ofquasi-contractive operators. It was shown in [29] that the Mann and Ishikawa iterationsare equivalent for the class of Zamfirescu operators. In 2006, Babu and Prasad [30]showed that the Mann...

... problems and variationalinequality problems. Taiwan J Math. 10, 1293–1303 (2006)18. Yao, Y, Liou, YC, Chen, R: Convergence theorems for fixed point problems and variational inequality problems ... variational inequality problems and fixed point problems. Appl Math Comput. 1906, 206–215 (2007)17. Ceng, LC, Yao, JC: Strong convergence theorem by an extragradient method for fixed point problems ... 2011:53http://www.fixedpointtheoryandapplications.com/content/2011/1/53Page 5 of 10RESEARC H Open Access Strong convergence of a hybrid method for monotone variational inequalities and fixed point problems Yonghong...