APPROXIMATION OF SOLUTIONS OF A GENERALIZED VARIATIONAL INEQUALITY PROBLEM BASED ON ITERATIVE METHODS Cho, Sun-Young;
In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.
Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory and Applications, 2014, 2014, 1, 94
Convergence theorems of solutions of a generalized variational inequality, Fixed Point Theory and Applications, 2011, 2011, 1, 19
An algorithm for treating asymptotically strict pseudocontractions and monotone operators, Fixed Point Theory and Applications, 2014, 2014, 1, 52
F. E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968), pp. 1-308. Amer. Math. Soc., Providence, R. I., 1976.
Y. J. Cho, S. M. Kang, and X. Qin, On systems of generalized nonlinear variational inequalities in Banach spaces, Appl. Math. Comput. 206 (2008), no. 1, 214-220.
Y. J. Cho and X. Qin, Systems of generalized nonlinear variational inequalities and its projection methods, Nonlinear Anal. 69 (2008), no. 12, 4443-4451.
Y. J. Cho and X. Qin, Generalized systems for relaxed cocoercive variational inequalities and projection methods in Hilbert spaces, Math. Inequal. Appl. 12 (2009), no. 2, 365-375.
H. Iiduka and W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005), no. 3, 341-350.
H. Iiduka, W. Takahashi, and M. Toyoda, Approximation of solutions of variational inequalities for monotone mappings, Panamer. Math. J. 14 (2004), no. 2, 49-61
M. A. Noor and Z. Huang, Some resolvent iterative methods for variational inclusions and nonexpansive mappings, Appl. Math. Comput. 194 (2007), no. 1, 267-275.
M. A. Noor, Some developments in general variational inequalities, Appl. Math. Comput. 152 (2004), no. 1, 199-277.
X. Qin and M. A. Noor, General Wiener-Hopf equation technique for nonexpansive mappings and general variational inequalities in Hilbert spaces, Appl. Math. Comput. 201 (2008), no. 1-2, 716-722.
G. Stampacchia, Formes bilineaires coercitives sur les ensembles convexes, C. R. Acad. Sci. Paris 258 (1964), 4413-4416.
T. Suzuki, Strong convergence of Krasnoselskii and Mann’s type sequences for oneparameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl. 305 (2005), no. 1, 227-239.
W. Takahashi and M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 118 (2003), no. 2, 417-428.
R. U. Verma, Generalized system for relaxed cocoercive variational inequalities and projection methods, J. Optim. Theory Appl. 121 (2004), no. 1, 203-210.
R. U. Verma, General convergence analysis for two-step projection methods and applications to variational problems, Appl. Math. Lett. 18 (2005), no. 11, 1286-1292.
H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. (2) 66 (2002), no. 1, 240-256.