Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems

Antipin A.S.: Methods for solving variational inequalities with related constraints. Comput. Math. Math. Phys. 40, 1239–1254 (2000)

Antipin A.S., Vasiliev F.P.: Regularized prediction method for solving variational inequalities with an inexactly given set. Comput. Math. Math. Phys. 44, 750–758 (2004)

Browder F.E.: Existence of periodic solutions for nonlinear equations of evolution. Proc. Nat. Acad. Sc. USA 55, 1100–1103 (1965)

Browder F.E., Petryshyn W.V.: Construction of fixed points of nonlinear mappings in Hilbert space. J. Math. Anal. Appl. 20, 197–228 (1967)

Ceng L.C., Yao J.C.: An extragradient-like approximation method for variational inequality problems and fixed point problems. Appl. Math. Comput. 190, 205–215 (2007)

Ceng L.C., Yao J.C.: On the convergence analysis of inexact hybrid extragradient proximal point algorithms for maximal monotone operators. J. Comput. Appl. Math. 217, 326–338 (2007)

Geobel K., Kirk W.A.: Topics on Metric Fixed-point Theory. Cambridge University Press, Cambridge, England (1990)

He B.-S., Yang Z.-H., Yuan X.-M.: An approximate proximal-extragradient type method for monotone variational inequalities. J. Math. Anal. Appl. 300, 362–374 (2004)

Hu S., Papageorgiou N.S.: Handbook of multivalued analysis, vol. I: theory. Kluwer Academic Publishers, Dordrecht (1997)

Iiduka H., Takahashi W.: Strong convergence theorem by a hybrid method for nonlinear mappings of nonexpansive and monotone type and applications. Adv. Nonlinear Var. Inequal. 9, 1–10 (2006)

Korpelevich G.M.: The extragradient method for finding saddle points and other problems. Matecon 12, 747–756 (1976)

Liu F., Nashed M.Z.: Regularization of nonlinear ill-posed variational inequalities and convergence rates. Set-Valued Anal. 6, 313–344 (1998)

Nadezhkina N., Takahashi W.: Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings. J. Optim. Theory Appl. 128, 191–201 (2006)

Nadezhkina N., Takahashi W.: Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings. SIAM J. Optim. 16, 1230–1241 (2006)

Nakajo K., Takahashi W.: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl. 279, 372–379 (2003)

Opial Z.: Weak convergence of the sequence of successive approximations for nonlinear mappings. Bull. Amer. Math. Soc. 73, 591–597 (1967)

Solodov M.V., Svaiter B.F.: An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions. Math. Oper. Res. 25, 214–230 (2000)

Takahashi W., Toyoda M.: Weak convergence theorems for nonexpansive mappings and monotone mappings. J. Optim. Theory Appl. 118, 417–428 (2003)

Zeng L.C., Yao J.C.: Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems. Taiwan J. Math. 10, 1293–1303 (2006)