Mehdi MOHAMMADI , G. Zamani ESKANDANI . A STRONG CONVERGENCE THEOREM FOR QUASI-EQUILIBRIUM PROBLEMS IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2022 , 42(1) : 221 -232 . DOI: 10.1007/s10473-022-0112-1

[1] Alber Y I. Metric and generalized projection operators in Banach spaces:Properties and applications//Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. Lecture Notes in Pure and Applied Mathematics, 178. New York:Marcel Dekker, 1996:15-50
[2] Alber Y I, Reich S. An iterative method for solving a class of nonlinear operator equations in Banach spaces. Panamer Math J, 1994, 4:39-54
[3] Aussel D, Cotrina J, Iusem A N. An existence result for qussi-equilibrium problems. J Convex Anal, 2017, 24:55-66
[4] Bianchi M, Schaible S. Generalized monotone bifunctions and equilibrium problems. J Optim Theory Appl, 1996, 90:31-43
[5] Butnariu D, Reich S, Zaslavski A J. Asymptotic behavior of relatively nonexpansive operators in Banach spaces. J Appl Anal, 2001, 7:151-174
[6] Chadli O, Chbani Z, Riahi H. Equilibrium problems with generalized monotone bifunctions and applications to variational inequalities. J Optim Theory Appl, 2000, 105:299-323
[7] Combettes P L, Hirstoaga S A. Equilibrium programming in Hilbert spaces. J Nonlinear Convex Anal, 2005, 6:117-136
[8] Djafari Rouhani B, Kazmi K R, Rizvi S H. A hybrid extragradient convex approximation method for a system of unrelated mixed equilibrium problems. Trans Math Program Appl, 2013, 1:82-95
[9] Djafari Rouhani B, Mohebbi V. Extragradient methods for quasi-equilibrium problems in Banach spaces. J Aust Math Soc, 2020, doi:10.1017/S1446788720000233
[10] Djafari Rouhani B, Mohebbi V. Proximal point method for quasi-equilibrium problems in Banach spaces. Numer Funct Anal Optim, 2020, 41:1007-1026
[11] Eskandani G Z, Raeisi M, Rassias T M. A hybrid extragradient method for solving pseudomonotone equilibrium problems using Bregman distance. J Fixed Point Theory Appl, 2018, 20(3):132
[12] Iusem A N, Kassay G, Sosa W. On certain conditions for the existence of solutions of equilibrium problems. Math Program, 2009, 116:259-273
[13] Iusem A N, Mohebbi V. Extragradient methods for nonsmooth equilibrium problems in Banach spaces. Optimization, 2020, 69:2383-2403
[14] Iusem A N, Mohebbi V. Extragradient methods for vector equilibrium problems in Banach spaces. Numer Funct Anal Optim, 2019, 40:993-1022
[15] Iusem A N, Sosa W. Iterative algorithms for equilibrium problems. Optimization, 2003, 52:301-316
[16] Iusem A N, Sosa W. On the proximal point method for equilibrium problems in Hilbert spaces. Optimization, 2010, 59:1259-1274
[17] Kamimura S, Takahashi W. Strong convergence of a proximal-type algorithm in a Banach space. SIAM J Optim, 2002, 13:938-945
[18] Kassay G, Reich S, Sabach S. Iterative methods for solving systems of variational inequalities in reflexive Banach spaces. SIAM J Optim, 2011, 21:1319-1344
[19] Khatibzadeh H, Mohebbi V. Approximating solutions of equilibrium problems in Hadamard spaces. Miskolc Math Notes, 2019, 20:281-297
[20] Khatibzadeh H, Mohebbi V. On the proximal point method for an infinite family of equilibrium problems in Banach spaces. Bull Korean Math Soc, 2019, 56:757-777
[21] Khatibzadeh H, Mohebbi V. Proximal point algorithm for infinite pseudo-monotone bifunctions. Optimization, 2016, 65:1629-1639
[22] Moudafi A. Proximal point algorithm extended to equilibrium problems. J Nat Geom, 1999, 15:91-100
[23] Raeisi M, Eskandani G Z. A hybrid extragradient method for a general split equality problem involving resolvents and pseudomonotone bifunctions in Banach spaces. Calcolo, 2019, 56(4):43
[24] Raeisi M, Chalack M, Eskandani G Z. Gradient projection-type algorithms for solving φ-strongly pseudomonotone equilibrium problems in Banach spaces. optimazation, to appear.
[25] Reem D, Reich S, De Pierro A. Re-examination of Bregman functions and new properties of their divergences. Optimization, 2019, 68:279-348
[26] Reich S. A weak convergence theorem for the alternating method with Bregman distances//Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. Lecture Notes in Pure and Applied Mathematics, 178. New York:Marcel Dekker, 1996:313-318
[27] Reich S, Sabach S. Three strong convergence theorems regarding iterative methods for solving equilibrium problems in reflexive Banach spaces//Optimization Theory and Related Topics, Contemp Math, 568, Israel Math Conf Proc. Providence, RI:Amer Math Soc, 2012:225-240
[28] Rockafellar R T. Characterization of the subdifferentials of convex functions. Pacific J Math, 1966, 17:497-510
[29] Rockafellar R T. On the maximal monotonicity of subdifferential mappings. Pacific J Math, 1970, 33:209-216
[30] Moharami R, Eskandani G Z. An extragradient algorithm for solving equilibrium problem and zero point problem in Hadamard spaces. RACSAM, 2020, 114:152
[31] Van N T T, Strodiot J J, Nguyen V H, Vuong P T. An extragradient-type method for solving nonmonotone quasi-equilibrium problems. Optimization, 2018, 67:651-664