[1] Alber Y I. Metric and generalized projection operator in Banach spaces: properties and applica-tions//Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. Vol 178 of Lecture Notes in Pure and Applied Mathematics. New York: Dekker, 1996: 15–50
[2] Aoyama K, Kimura Y, Takahashi W, Toyoda M. Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space. Nonlinear Anal, 2006, 67: 2350–2360
[3] 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
[4] Bauschke H H, Borwein J M. Legendre functions and the method of random Bregman projections. J Convex Anal, 1997, 4: 27–67
[5] Bauschke H H, Borwein J M, Combettes P L. Bregman monotone optimization algorithms. SIAM J Control Optim, 2003, 42: 596–636
[6] Bauschke H H, Wang X, Yao L. General resolvents for monotone operators: characterization and exten-sion//Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems. Madison, WI: Medical Physics Publishing, 2009: 57–74
[7] Bello Cruz J Y, Iusem A N. An explicit algorithm for monotone variational inequalities. Optimization, 2012, 61(7): 855–871
[8] Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Student, 1994, 63: 123–145
[9] Bonnans J F, Shapiro A. Perturbation Analysis of Optimization Problems. New York: Springer, 2000
[10] Borwein J M, Reich S, Sabach S. A characterization of Bregman firmly nonexpansive operators using a new
monotonicity concept. J Nonlinear Convex Anal, 2011, 12: 161–184
[11] 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 and Math Phys, 1967, 7: 200–217
[12] Butnariu D, Resmerita E. Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces. Abstr Appl Anal, 2006, 2006: Art ID 84919
[13] Butnariu D, Iusem A N. Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization. Dordrecht: Kluwer Academic Publishers, 2000
[14] Butnariu D, Censor Y, Reich S. Iterative averaging of entropic projections for solving stochastic convex feasibility problems. Comput Optim Appl, 1997, 8: 21–39
[15] Censor Y, Lent A. An iterative row-action method for interval convex programming. J Optim Theory Appl, 1981, 34: 321–353
[16] Censor Y, Reich S. Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization. Optimization, 1996, 37: 323–339
[17] Chen J W, Cho Y J, Agarwal R P. Strong convergence theorems for equilibrium problems and weak Bregman relatively nonexpansive mappings in Banach spaces. J Ineq Appl, 2013, 2013: 119
[18] Chen J W, Wan Z, Yuan L. Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces. Int J Math Math Sci, 2011, 2011: 1–3
[19] Combettes P L, Hirstoaga S A. Equilibrium programming in Hilbert spaces. J Nonlinear Convex Anal, 2005, 6: 117–136
[20] Kohsaka F, Takahashi W. Proximal point algorithms with Bregman functions in Banach spaces. J Nonlinear Convex Anal, 2005, 6: 505–523
[21] 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
[22] Maing´e P E. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-Valued Anal, 2008, 16: 899–912
[23] Martin-Marquez V, Reich S, Sabach S. Right Bregman nonexpansive operators in Banach spaces. Nonlinear
Analysis, 2012, 75: 5448–5465
[24] Martin-Marquez V, Reich S, Sabach S. Iterative methods for approximating fixed points of Bregman non-expansive operators. Discrete and Continuous Dynamical Systems, 2013, 6: 1043–1063
[25] Moreau J -J. Sur la fonction polaire dune fonction semi-continue superieurement. C R Acad Sci Paris, 1964, 258: 1128–1130
[26] Moudafi A. A partial complement method for approximating solutions of a primal dual fixed-point problem. Optim Lett, 2010, 4(3): 449–456
[27] Pardalos P M, Rassias T M, Khan A A, eds. Nonlinear Analysis and Variational Problems. Springer, 2010
[28] Phelps R P. Convex Functions, Monotone Operators, and Differentiability. 2nd ed. Berlin: Springer Verlag, 1993
[29] 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
[30] 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
[31] Qin X, Su Y. Strong convergence theorems for relatively nonexpansive mappings in a Banach space. Non-linear Anal, 2007, 67: 1958–1965
[32] Reich S. A weak convergence theorem for the alternating method with Bregman distances//Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. New York: Marcel Dekker, 1996: 313–318
[33] Reich S, Sabach S. Existence and approximation of fixed points of Bregman firmly nonexpansive opera-tors in reflexive Banach spaces//Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Optimization and its Applications, Vol 49. New York: Springer, 2011: 301–316
[34] Reich S, Sabach S. A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces. J Nonlinear and Convex Analysis, 2009, 10(3): 471–485
[35] Reich S, Sabach S. Two strong convergence theorems for a proximal method in reflexive Banach spaces. Numerical Functional Analysis and Optimization, 2010, 31(1): 22–44
[36] Reich S, Sabach S. Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces. Nonlinear Anal, 2010, 73(1): 122–135
[37] Reich S, Sabach S. A projection method for solving nonlinear problems in reflexive Banach spaces. J Fixed Point Theory Appl, 2011, 9(1): 101-116
[38] Rockafellar R T. Level sets and continuity of conjugate convex functions. Trans Amer Math Soc, 1966, 123: 46–63
[39] 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
[40] Suantai S, Cho Y J, Cholamjiak P. Halpern´s iteration for Bregman strongly nonexpansive mappings in reflexive Banach spaces. Comp Math Appl, 2012, 64: 489–499
[41] 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
[42] Takahashi W, Zembayashi K. Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings. Fixed Point Theory Appl, 2008, 2008: Article ID 528476
[43] TakahashiW, Zembayashi K. Strong and weak convergence theorems for equilibrium problems and relatively
nonexpansive mappings in Banach spaces. Nonlinear Anal, 2009, 70: 45–57
[44] Wangkeeree R. An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings. Fixed Point Theory and Applications, 2008, 2008: Article ID 134148
[45] Xu H K. Iterative algorithms for nonlinear operators. J London Math Soc, 2002, 66(2): 240–256
[46] C. Zalinescu; Convex Analysis in General Vector Spaces. River Edge, NJ: World Scientific, 2002
[47] Zegeye H, Ofoedu E U, Shahzad N. Convergence theorems for equilibrium problems, variational inequality problem and countably infinite relatively nonexpansive mappings. Appl Math Comp, 2010, 216: 3439–3449
[48] Zegeye H, Shahzad N. A hybrid scheme for finite families of equilibrium, variational inequality and fixed point problems. Nonlinear Anal, 2010, 70: 2707–2716
[49] Zhu J H, Chang S S. Halpern-Manns iterations for Bregman strongly nonexpansive mappings in reflexive Banach spaces with applications. J Ineq Appl, 2013, 2013: 146 |