A GENERALIZED MEAN PROXIMAL ALGORITHM FOR SOLVING GENERALIZED MIXED EQUILIBRIUM PROBLEMS

被引：0
|
作者：
Saddeek, A. M. [1 ]
机构：
[1] Assiut Univ, Dept Math, Fac Sci, Assiut, Egypt
来源：
BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 7卷 / 01期
关键词：
Generalized mean proximal algorithm; generalized mixed equilibrium problem; generalized resolvent mapping; theta-pseudomonotone mapping; delta- Lipschitz continuous mapping; convergence; Hilbert space; fixed point;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In a recent paper [14], the fixed point and resolvent techniques have been used to give an iterative algorithm for solving generalized mixed equilibrium problem (GMEP). In this paper, an extended iterative algorithm, called generalized mean proximal algorithm (GMPA) is presented and its convergence to the solution of GMEP with theta-pseudomonotne and delta- Lipschitz continuous mappings in Hilbert spaces is proved. Our approach is based on the basic notions of generalized resolvents and fixed points. The results improve and extend important recent results.
引用
收藏
页码：1 / 11
页数：11
相关论文
共 50 条
  • [1] An Iterative Algorithm for Solving Generalized Equilibrium Problems and Fixed Points Problems
    Li, Mengqin
    Yao, Yonghong
    Liou, Yeong-Cheng
    [J]. INTERNATIONAL JOINT CONFERENCE ON COMPUTATIONAL SCIENCES AND OPTIMIZATION, VOL 2, PROCEEDINGS, 2009, : 792 - +
  • [2] On a generalized proximal point method for solving equilibrium problems in Banach spaces
    Burachik, Regina
    Kassay, Gabor
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (18) : 6456 - 6464
  • [3] A NEW ITERATIVE ALGORITHM FOR SOLVING A SYSTEM OF GENERALIZED EQUILIBRIUM PROBLEMS
    Abkar, A.
    Shekarbaigi, M.
    Aghamohammadi, N.
    [J]. JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2018,
  • [4] NEW ITERATIVE ALGORITHM FOR SOLVING A SYSTEM OF GENERALIZED MIXED IMPLICIT EQUILIBRIUM PROBLEMS IN BANACH SPACES
    Ding, Xie-Ping
    Ho, Juei-Ling
    [J]. TAIWANESE JOURNAL OF MATHEMATICS, 2011, 15 (02): : 673 - 695
  • [5] Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems
    Ceng, Lu-Chuan
    Wen, Ching-Feng
    [J]. JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2012,
  • [6] Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space
    Ceng, Lu-Chuan
    Kum, Sangho
    Yao, Jen-Chih
    [J]. FIXED POINT THEORY AND APPLICATIONS, 2010,
  • [7] Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space
    Lu-Chuan Ceng
    Sangho Kum
    Jen-Chih Yao
    [J]. Fixed Point Theory and Applications, 2010
  • [8] Hybrid Iterative Method for Solving a System of Generalized Equilibrium Problems, Generalized Mixed Equilibrium Problems and Common Fixed Point Problems in Hilbert Spaces
    Rodjanadid, Benjawan
    [J]. THAI JOURNAL OF MATHEMATICS, 2015, 13 (03): : 737 - 763
  • [9] GENERALIZED PROXIMAL DISTANCES FOR BILEVEL EQUILIBRIUM PROBLEMS
    Bento, G. C.
    Cruz Neto, J. X.
    Lopes, J. O.
    Soares, P. A., Jr.
    Soubeyran, A.
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2016, 26 (01) : 810 - 830
  • [10] Solving a Class of Generalized Nash Equilibrium Problems
    Peiyu LI
    Guihua LIN
    [J]. Journal of Mathematical Research with Applications, 2013, (03) : 372 - 378
12345