New relaxed hybrid-extragradient method for fixed point problems, a general system of variational inequality problems and generalized mixed equilibrium problems

References

• Acedo , GL and Xu , HK . 2007 . Iterative methods for strict pseudo-contractions in Hilbert spaces . Nonlinear Anal. , 67 : 2258 – 2271 .
   Web of Science ®Google Scholar
• Aslam Noor , M . 2004 . Some developments in general variational inequalities . Appl. Math. Comput. , 152 : 199 – 277 .
   Web of Science ®Google Scholar
• Blum , E and Oettli , W . 1994 . From optimization and variational inequalities to equilibrium problems . Math. Student , 63 : 123 – 145 .
   Google Scholar
• Ceng , LC , Al-Homidan , S , Ansari , QH and Yao , JC . 2009 . An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings . J. Comput. Appl. Math. , 223 : 967 – 974 .
   Web of Science ®Google Scholar
• Ceng , LC , Wang , C and Yao , JC . 2008 . Strong convergence theorems by a rlaxed extragradient method for a general system of variational inequalities . Math. Meth. Oper. Res. , 67 : 375 – 390 .
   Web of Science ®Google Scholar
• Ceng , LC and Yao , JC . 2008 . A hybrid iterative scheme for mixed equilibrium problems and fixed point problems . J. Comput. Appl. Math. , 214 : 186 – 201 .
   Web of Science ®Google Scholar
• Censor , Y , Iusem , AN and Zenios , SA . 1998 . An interior point method with Bregman functions for the variational inequality problem with paramonotone operators . Math. Program. , 81 : 373 – 400 .
   Web of Science ®Google Scholar
• Combettes , PL and Hirstoaga , SA . 1997 . Equilibrium programming using proximal-like algorithms . Math. Program. , 78 : 29 – 41 .
   Google Scholar
• Korpelevich , GM . 1976 . An extragradient method for finding saddle points and for other problems . Ekonomika i Matematicheskie Metody , 12 : 747 – 756 .
   Google Scholar
• Moudafi , A . 2008 . Weak convergence theorems for nonexpansive mappings and equilibrium problems . J. Nonlinear Convex Anal. , 9 : 37 – 43 .
   Web of Science ®Google Scholar
• Moudafi , A and Théra , M . 1999 . “ Proximal and Dynamical Approaches to Equilibrium Problems ” . In Lecture Notes in Economics and Mathematical Systems , Vol. 477 , 187 – 201 . Berlin : Springer-Verlag .
   Google Scholar
• Nadezhkina , N and Takahashi , W . 2006 . Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings . J. Optim. Theory Appl. , 128 : 191 – 201 .
   Web of Science ®Google Scholar
• Peng , JW and Yao , JC . 2008 . A new hybrid-extragradient method for generalized mixed euqilibrium problems, fixed point problems and variational inequality problems . Taiwanese J. Math. , 12 : 1401 – 1432 .
   Web of Science ®Google Scholar
• Suzuki , T . 2005 . Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals . J. Math. Anal. Appl. , 305 : 227 – 239 .
   Web of Science ®Google Scholar
• Takahashi , S and Takahashi , W . 2007 . Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces . J. Math. Anal. Appl. , 331 : 506 – 515 .
   Web of Science ®Google Scholar
• Takahashi , S and Takahashi , W . 2008 . Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space . Nonlinear Anal. , 69 : 1025 – 1033 .
   Web of Science ®Google Scholar
• Takahashi , W and Toyoda , M . 2003 . Weak convergence theorems for nonexpansive mappings and monotone mappings . J. Optim. Theory Appl. , 118 : 417 – 428 .
   Web of Science ®Google Scholar
• Verma , RU . 1999 . On a new system of nonlinear variational inequalities and associated iterative algorithms . Math. Sci. Res. Hot-line , 3 : 65 – 68 .
   Google Scholar
• Yamada , I . 2001 . “ The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed point sets of nonexpansive mappings ” . In Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications , Edited by: Butnariu , D , Censor , Y and Reich , S . 473 – 504 . Amsterdam, , Holland : North-Holland .
   Google Scholar
• Yao , JC . 1994 . Variational inequalities and generalized monotone operators . Math. Oper. Res. , 19 : 691 – 705 .
   Web of Science ®Google Scholar
• Yao , JC and Chadli , O . 2005 . “ Pseudomonotone complementarity problems and variational inequalities ” . In Handbook of Generalized Convexity and Monotonicity , Edited by: Couzeix , JP , Haddjissas , N and Schaible , S . 501 – 558 . Berlin : Springer .
   Google Scholar
• Yao , Y and Yao , JC . 2007 . On modified iterative method for nonexpansive mappings and monotone mappings . Appl. Math. Comput. , 186 : 1551 – 1558 .
   Web of Science ®Google Scholar
• Zeng , LC , Schaible , S and Yao , JC . 2005 . Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequalities . J. Optim. Theory Appl. , 124 : 725 – 738 .
   Web of Science ®Google Scholar
• Zeng , LC and Yao , JC . 2006 . Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems . Taiwanese J. Math. , 10 : 1293 – 1303 .
   Web of Science ®Google Scholar
• Zeng , LC and Yao , JC . 2008 . Mixed projection methods for systems of variational inequalities . J. Global Optim. , 41 : 465 – 478 .
   Google Scholar