Nonlinear algorithms for a common solution of a system of variational inequalities, a split equilibrium problem and fixed point problems
Main Article Content
Abstract
Article Details
References
[1] Q. H. Ansari, C. S. Lalitha and M. Mehta, Generalized Convexity, Nonsmooth Variational Inequalities and Nonsmooth Optimization, CRC Press, Boca Raton, 2014. Google Scholar
[2] Q. H. Ansari, N. C. Wong and J. C. Yao, The existence of nonlinear inequalities, Appl. Math Lett. 12 (1999), 89–92. Google Scholar
[3] E. Blum and W. Cettli, From optimization and variational inequalities to equi- librium problems, Math. Stud. 63 (1994), 123–145. Google Scholar
[4] A. Bnouhachem, A self-adaptive method for solving general mixed variational inequalities, J. Math. Anal. Appl. 309 (2005), 136–150. Google Scholar
[5] A. Bnouhachem, A new projection and contraction method for linear variational inequalities, J. Math. Anal. Appl. 314 (2006), 513–525. Google Scholar
[6] N. Buong and L. T. Duong, An explicit iterative algorithm for a class of vari- ational inequalities in Hilbert spaces, J. Optim. Theory Appl. 151 (2011), 513– 524. Google Scholar
[7] L. C. Ceng, Q. H. Ansari, S. Schaible and J. C. Yao, Iterative methods for gener- alized equilibrium problems, systems of general generalized equilibrium problems and fixed point problems for nonexpansive mappings in Hilbert spaces, Fixed Point Theory 12 (2011), 293–308. Google Scholar
[8] L. C. Ceng, Q. H. Ansari and J. C. Yao, Some iterative methods for finding fixed points and for solving constrained convex minimiization problems, Nonlin- ear Anal. 74 (2011), 5286–5302. Google Scholar
[9] L. C. Ceng, C. Y. Wang and J. C. Yao, Strong convergence theorems by a re- laxed extragradient method for a general system of variational inequalities, Math Methods Oper. Res. 67 (2008), 375-390. Google Scholar
[10] L. C. Ceng and J. C. Yao, A relaxed extragradient-like method for a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem, Nonlinear Anal. 72 (2010), 1922-1937. Google Scholar
[11] Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projec- tions in a product space, Numer. Algorithms 8 (1994), 221–239. Google Scholar
[12] S. S. Chang, H. W. J. Lee and C. K. Chan, A new method for solving equilibrium problem, fixed point problem and variational inequality problem with application to optimization, Nonlinear Anal. 70 (2009), 3307–3319. Google Scholar
[13] F. Cianciaruso, G. Marino, L. Muglia and Y. Yao, A hybrid projection algo- rithm for finding solutions of mixed equilibrium problem and variational inequal- ity problem, Fixed Point Theory Appl. 2010, 2010: 383740. Google Scholar
[14] P. L. Combetters and S. A. Hirstoaga, Equilibrium programming using proximal like algorithms, Math. Program. 78 (1997), 29–41. Google Scholar
[15] P. Duan and S. He, Generalized viscosity approximation methods for nonexpan- sive mappings, Fixed Point Theory Appl. 2014, 2014: 68. Google Scholar
[16] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Stud. Adv. Math. vol.28, Cambridge University Press, Cambridge, 1990. Google Scholar
[17] G. L opez, V. Martin and H. K. Xu, Iterative algorithm for the multiple-sets split feasibility problem, In: Biomedical Mathematics Promising Directions: In Imaging Therapy Planning and Inverse Problems, pp. 243-279, 2009. Google Scholar
[18] P. E. Mainge and A. Moudafi, Strong convergence of an iterative method for hierarchical fixed point problems, Pac. J. Optim. 3 (2007), 529–538. Google Scholar
[19] X. Qin, M. Shang and Y. Su, A general iterative method for equilibrium problem and fixed point in Hilbert spaces, Nonlinear Anal. 69 (2008), 3897–3909. Google Scholar
[20] T. Suzuki, Strong convergence of Krasnoselskii and Mann’s type sequences for one parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl. 35 (2005), 227–239. Google Scholar
[21] N. Suzuki, Moudafi’s viscosity approximations with Meir-Keeler contractions, J. Math. Anal. Appl. 325 (2007), 342–352. Google Scholar
[22] M. Tian, A general iterative algorithm for nonexpansive mappings in Hilbert spaces, Nonlinear Anal. 73 (2010), 689–694. Google Scholar
[23] R. U. Verma, Projection methods, algorithms and a new system of nonlinear variational inequalities, Comput. Math. Appl. 41 (2001), 1025–1031. Google Scholar
[24] R. U. Verma, General convergence analysis for two-step projection methods and applications to variational problems, Appl. Math. Lett. 18 (2005), 1286–1292. Google Scholar
[25] H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory and Appl. 116 (2003), 659–678. Google Scholar
[26] I. Yamada, The hybrid steepest descent method for the variational inequality problems over the intersection of fixed points sets of nonexpansive mapping. In: D. Butnariu, Y. Censor, S. Reich (eds). Inherently Parallel Algorithms in Fea- sibility and Optimization and Their Application, pp. 473–504, North-Holland, Amsterdam, 2001. Google Scholar
[27] C. Zhang and C. Yang, A new explicit iterative algorithm for solving a class of variational inequalities over the common fixed points set of a finite family of nonexpansive mappings, Fixed Point Theory Appl. 2014, 2014: 60. Google Scholar
[28] H. Y. Zhou and P. A. Wang, A simpler explicit iterative algorithm for a class of variational inequalities in Hilbert spaces, J. Optim. Theory Appl. 161 (2014), 716–727. Google Scholar