Sheng ZHU , Jianhua HUANG . STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2016 , 36(5) : 1433 -1444 . DOI: 10.1016/S0252-9602(16)30079-0

[1] Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Stud, 1994, 63:123-145
[2] Moudafi A. A partial complement method for approximating solutions of a primal dual fixed-point problem. Optim Lett, 2010, 4(3):449-456
[3] Pardalos P M, Rassias T M, Khan A A. Nonlinear Analysis and Variational Problems. Springer, 2010
[4] Zegeye H, Ofoedu E U, Shahzad N. Convergence theorems for equilibrium problems, variational inequality problem andcountably infinite relatively nonexpansive mappings. Appl Math Comp, 2010, 216:3439-3449
[5] Bello-Cruz J Y, Iusem A N. An explicit algorithm for monotone variational inequalities. Optimization, 2012, 7(61):855-877
[6] Chen J W, Cho Y J, Agwal R P. Strong convergence theorems for equilibrium problems and weak Bregman relativelynonexpansive mappings in Banach spaces. J Ineq Appl, 2013, Art ID:119
[7] Kumam P. A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping. J Appl Math Comput, 2009, 29:263-280
[8] Plubtieng S, Punpaeng R. A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings. Appl Math Comput, 2008, 197:548-558
[9] Qin X, Cho Y J, Kang S M. Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces. J Comput Appl Math, 2009, 225:20-30
[10] Qin X, Su Y. Strong convergence theorems for relatively nonexpansive mappings in a Banach space. Nonlinear Anal, 2007, 67:1958-1965
[11] Shehu Y. A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces. J Glob Optim, 2012, 54:519-535
[12] Takahashi W, Zembayashi K. Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings. Fixed Point Theory Appl, 2008
[13] Takahashi W, Zembayashi K. Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces. Nonlinear Anal, 2000, 70:45-57
[14] Wangkeeree R. An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings. Fixed Point Theory Appl, 2008, Art ID:528476
[15] Xu H K. Iterative algorithms for nonlinear operators. J London Math Soc, 2002, 66(2):240-256
[16] Bregman L M. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput Math Math Phys, 1967, 7:200-217
[17] Bauschke H H, Borwein J M, Combettes P L. Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces. Comm Contemp Math, 2001, 3:615-647
[18] Takahashi S, Takahashi W. Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces. J Math Anal Appl, 2007, 331:506-518
[19] Butnariu D, Resmerita E. Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces. Abstr Appl Anal, 2006, Art ID:84919
[20] Browder F E. Fixed point theorems for noncompact mappings in Hilbert space. Proc Natl Acad Sci, USA, 1965, 53:1272-1276
[21] Halpern B. Fixed points of nonexpanding maps. Bull Am Math Soc, 1967, 73:957-961
[22] Martinez-Yanes C, Xu H K. Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal, 2006, 64:2400-2411
[23] Qin X L, Cho Y J, Kang S M, Zhou H Y. Convergence of a modified Halpern-type iterative algorithm for (quasi) nonexpansive mappings. Appl Math Lett, 2009, 22:1051-1055
[24] Wang Z M, Su Y F, Wang D X, Dong Y C. A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces. J Comput Appl Math, 2011, 235:2364-2371
[25] Su Y F, Xu H K, Zhang X. Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications. Nonlinear Anal, 2010, 73:3890-3906
[26] Kang J, Su Y, Zhang X. Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications. Nonlinear Anal, HS, 2010, 4(4):755-765
[27] Chang S S, Joseph-Lee H W, Chan C K. A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications. Nonlinear Anal, TMA, 2010, 73(7):2260-2270
[28] Chang S S, Chan C K, Joseph-Lee H W. Modified Block iterative algorithm for quasi-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces. Appl Math Comput, 2011, 217:7520-7530
[29] Nilsrakoo W, Saejung S. Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces. Appl Math Comput, 2011, 217(14):6577-6586
[30] Huang Y Y, Jeng J C, Kuo T Y, Hong C C. Fixed point and weak convergence theorems for point-dependent λ-hybrid mappings in Banac spaces. Fixed Point Theory Appl, 2011, Art ID:105
[31] Chang S S, Wang L, Wang X R, Chan C K. Strong convergence theorems for Bregman totally quasiasymptotically nonexpansive mappings in reflexive Banach spaces. Appl Math Comput, 2014, 228:38-48
[32] Reich S, Sabach S. Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces. Nonlinear Anal, 2010, 73:122-135
[33] Censor Y, Lent A. An iterative row-action method for interval convex programing. J Optim Theory Appl, 1981, 34:321-353
[34] Butnariu D, Iusem A N. Totally convex functions for fixed points computation and infinite dimensional optimization//Applied Optimization, Vol 40. Dordrecht:Kluwer Academic, 2000
[35] Reich S, Sabach S. Two strong convergence theorems for a proximal method in reflexive Banach spaces. Numer Funct Anal Optim, 2010, 31:22-44
[36] Combettes P L, Hirstoaga S A. Equilibrium programming in Hilbert spaces. J Nonlinear Convex Anal, 2005, 6:117-136
[37] Kassay G, Reich S, Sabach S. Iterative methods for solving systems of variatio nal inequalities in reflexive Banach spaces. SIAM J Optim, 2011, 21:1319-1344
[38] Wang S H, Kang S M. Strong convergence iterative algorithms for equilibrium problems and fixed point problems in Banach spaces. Abs Appl Anal, 2013, Art ID:618762