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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 67, 2018 - Issue 12
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Articles

New algorithms for solving system of generalized mixed equilibrium problems and some nonlinear problems, with applications

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Pages 2325-2345 | Received 27 Jul 2017, Accepted 22 Oct 2018, Published online: 15 Nov 2018

References

  • Alber Ya. Metric and generalized projection operators in Banach spaces: properties and applications. In Kartsatos AG, editor. Theory and applications of nonlinear operators of accretive and monotone type. New York: Marcel Dekker; 1996. p. 15–50.
  • Kamimura S, Takahashi W. Strong convergence of a proximal-type algorithm in a Banach space. SIAM J Optim. 2002;13(3):938–945. doi: 10.1137/S105262340139611X
  • Reich S. A weak convergence theorem for the alternating method with Bergman distance. In Kartsatos AG, editor. Theory and applications of nonlinear operators of accretive and monotone type. New York: Dekler; 1996. p. 313–318. (Lecture notes in Pure and appl. Math.; vol. 178).
  • Feng Q, Su Y, Yan F. Modified hybrid block iterative algorithm for uniformly quasi-φ-nonexpansive mappings. Abs Appl Anal. 2012;2012. doi:10.1155/2012/215261.
  • Saewan S. Strong convergence theorem for total quasi-φ-asymptotically nonexpansive maps in Banach space. Fixed Point Theory and Appl. 2013;2013:297. doi: 10.1186/1687-1812-2013-297
  • Ofoedu EU, Malonza DM. Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type. Appl Math Comput. 2011;217:6019–6030. doi:10.1016/j.amc.2010.12.073
  • Deng W-Q. An iterative solution to a system of nonlinear Hammerstein type equations and a sytem of generalized mixed equilibrium problems. J Fixed Point Theory Appl. doi:10.1007/s11784-016-0389-6
  • Wang XR, Chang SS, Wang L, et al. Strong convergence theorems for nonlinear operator equations with total quasi-φ-asymptotically nonexpansive mappings and applications. Fixed Point Theory Appl. doi:10.1186/1687-1812-2012-34
  • Plubtieng S, Ungchittrakool K. Approximation of common fixed points for a countable family of relatively nonexpansive mappings in a Banach space and applications. Nonlinear Anal. 2010;72(6):2896–2908. doi: 10.1016/j.na.2009.11.034
  • Ungchittrakool K, Jarernsuk A. Strong convergence by a hybrid algorithm for solving generalized mixed equilibrium problems and fixed point problems of a Lipschitz pseudo- contraction in Hilbert spaces. Fixed Point Theory Appl. doi:10.1186/1687-1812-2012-147
  • Ungchittrakool K. An iterative shrinking projection method for solving fixed point problems of closed and φ-quasi-strict pseudo-contractions along with generalized mixed equilibrium problems in Banach spaces. 2012;2012:Article ID 536283, 20 pages.
  • Zegeye H, Ofoedu EU, Shahzad N. Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings. Appl Math Comput. 2010;216(12):3439–3449.
  • Zegeye H, Shahzad N. Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings. Nonlinear Anal. 2009;70(7):2707–2716. doi: 10.1016/j.na.2008.03.058
  • Zegeye H, Shahzad N. A hybrid scheme for finite families of equilibrium, variational inequality and fixed point problems. Nonlinear Anal. 2011;74:263–272. doi: 10.1016/j.na.2010.08.040
  • Zhang SS. On the generalized mixed equilibrium problem in Banach space. Appl Math Mech. 2009;30(9):1105–1112. doi: 10.1007/s10483-009-0904-6
  • Su YF, Xu HK, Zhang X. Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications. Nonlinear Anal. 2010;73:3890–3906. doi:10.1016/j.na.2010.08.021
  • Qin X, Cho SY, Kang SM. Strong convergence of shrinking projection methods for quasi-φ-nonexpansive mappings and equilibrium problems. J Comput Appl Math. 2010;234(3):750–760. doi: 10.1016/j.cam.2010.01.015
  • Xu HK. Inqualities in Banach spaces with applications. Nonlinear Anal. 1991;16:1127–1138. doi:10.1016/0362-546X(91)90200-K
  • Chang SS, Wang L, Tang YK, et al. Strong convergence theorems of nonlinear operator equations for countable family of multi-valued total quasi-φ-asymptotically nonexpansive mappings with applications. Fixed Point Theory Appl. 2012;2012:69. doi: 10.1186/1687-1812-2012-69
  • Deng WQ, Bai P. An implicit iteration process for common fixed points of two infinite families of asymptotically nonexpansive mappings in Banach spaces. J Appl Math. 2013;2013:602582. doi:10.1155/2013/602582
  • Alber Ya, Ryazantseva I. Nonlinear ill posed problems of monotone-type. London (UK): Springer; 2006.

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