RESEARCH ARTICLE Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings

... results involving general viscosity approximation processes for nonexpansive mapping, nonexpansive semigroup, and contractive mapping to nonexpansive semigroup and φ-strongly pseudocontractive mapping ... 3.1 and 3.2 are valid for nonexpansive mappings Thus, we have the following mean ergodic assertions of general viscosity iteration process for nonexpansive mappin...

Ngày tải lên: 21/06/2014, 07:20

... no 9, pp 3307–3319, 2009 Y J Cho, X Qin, and J I Kang, “Convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems, ” Nonlinear Analysis: Theory, Methods ... 2009 C Jaiboon, W Chantarangsi, and P Kumam, “A convergence theorem based on a hybrid relaxed extragradient method for generalized equilibrium problems and fixed...

Ngày tải lên: 21/06/2014, 07:20

... Mathematics and Computation, vol 186, no 2, pp 1551–1558, 2007 17 Y Su, M Shang, and X Qin, “An iterative method of solution for equilibrium and optimization problems, ” Nonlinear Analysis: Theory, Methods ... points problems, equilibrium points problems, and variational inequalities problems Therefore, the constrained set F : Fix S ∩EP F ∩VI C, B is very important a...

Ngày tải lên: 21/06/2014, 07:20

... fixed points of nonlinear mappings is an important and active research area In particular, iterative algorithms for finding fixed points of nonexpansive mappings have received vast investigation ... fixed points of a countable family of nonexpansive mappings in a Banach space,” Nonlinear Analysis: Theory, Methods & Applications, vol 67, no 8, pp 2350–2360, 20...

Ngày tải lên: 21/06/2014, 11:20

... element of the solutions set of a system of equilibrium problems, fixed points set of a family of infinitely nonexpansive mappings, and the solution set of a variational inequality for a relaxed coercive ... J.-W Peng and J.-C Yao, A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappi...

Ngày tải lên: 21/06/2014, 11:20

... a major error in the original version of this paper References K Aoyama, Y Kimura, W Takahashi, and M Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings ... Banach space with a uniformly G´ teaux differentiable norm a Other investigations of approximating common fixed points for a countable family of nonexpansive...

Ngày tải lên: 21/06/2014, 11:20

... spaces,” Journal of Mathematical Analysis and Applications, vol 325, no 1, pp 469–479, 2007 18 Fixed Point Theory and Applications 17 E Blum and W Oettli, “From optimization and variational ... solutions of equilibrium and fixed point problems, ” Journal of Mathematical Analysis and Applications, vol 344, no 1, pp 340– 352, 2008 20 S.-S Chang, H W Joseph Lee, and...

Ngày tải lên: 21/06/2014, 11:20

... 2007 27 R Wangkeeree, “An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings,” Fixed Point Theory and Applications, ... 2445–2457, 2008 L.-C Ceng and J.-C Yao, “An extragradient- like approximation method for variational inequality problems and fixed point problems, ” A...

Ngày tải lên: 21/06/2014, 20:20

... Zeng and Yao 16 introduced a new hybrid iterative algorithm for mixed equilibrium problems and fixed point problems and Mainge and Moudafi 22 introduced an iterative algorithm for equilibrium problems ... theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings,” Fixed Point Theory and Applications, vol 200...

Ngày tải lên: 21/06/2014, 20:20

... “Some iterative techniques for general monotone variational inequalities,” Optimization, vol 46, no 4, pp 391–401, 1999 20 M A Noor, “Some algorithms for general monotone mixed variational inequalities,” ... that T is monotone if and only of for each ρ > 0, the T resolvent Jρ is nonexpansive, and T is maximal monotone if and only of for each ρ > 0, the T resolvent Jρ i...

Ngày tải lên: 21/06/2014, 20:20

... of two variational inequalities VI C ,A and VI C,B PC ; solution of a system of two mixed equilibrium problems Tn Trn and Vn solution of a mixed equilibrium problem and a variational inequality ... prove a strong convergence theorem to approximate a fixed point of S that is also a solution of a mixed equilibrium problem and a solution...

Ngày tải lên: 21/06/2014, 20:20

... for finding a common fixed point of a finite family of relatively nonexpansive mappings in Banach spaces by using the hybrid method in mathematical programming Theorem 3.1 Let E be a uniformly convex ... family of relatively nonexpansive mappings in Banach spaces,” Fixed Point Theory and Applications, vol 2007, Article ID 21972, 18 pages, 2007 24 M Kik...

Ngày tải lên: 21/06/2014, 23:20

... operator equations in Banach spaces,” Panamerican Mathematical Journal, vol 4, no 2, pp 39–54, 1994 12 S Kamimura and W Takahashi, Strong convergence of a proximal-type algorithm in a Banach space,” ... S Matsushita and W Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space,” Journal of Approximation Theory, vol 134...

Ngày tải lên: 22/06/2014, 11:20

... extragradient type method for a system of equilibrium problems, variational inequality problems and fixed points of finitely many nonexpansive mappings, Journal of Nonlinear Analysis and Optimization, ... Plubtieng and K Ungchittrakool, Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings...

Ngày tải lên: 14/10/2015, 08:18

... of nonexpansive mappings {Sj }j=1 in Hilbert spaces, namely: • a parallel hybrid Mann -extragradient method; • a parallel hybrid Halpern -extragradient method, and • a parallel hybrid iteration -extragradient ... Parallel hybrid methods for a finite family of relatively nonexpansive mappings Numer Funct Anal Optim 35(6) (2014), pp 649-664 [3] P.K Anh, D.V Hieu...

Ngày tải lên: 14/10/2015, 08:21