참고문헌
- Y.I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, in: A.G. Kartsatos (Ed.), Theory and Applications of Nonlinear Operator of Accretive and Monotone Type, Marcel Dekker, New York, (1996) 15-50.
- M. Aslam Noor, Generalized mixed quasi-equilibrium problems with trifunction, Appl. Math. Lett. 18 (2005) 695-700. https://doi.org/10.1016/j.aml.2004.04.015
- M. Aslam Noor, W. Oettli, On general nonlinear complementarity problems and quasi equilibria, Matematiche (Catania) 49 (1994) 313-331.
- E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994) 123-145.
- H. H. Bauschke, J. M. Borwein, P. L. Combettes, Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces, Commun. Contemp. Math. 3 (2001) 615-647. https://doi.org/10.1142/S0219199701000524
- J. F. Bonnans, A. Shapiro, Perturbation Analysis of Optimization Problem, Springer, NewYork (NY), 2000.
- R.E. Bruck, S. Reich, Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math. 3 (1977) 459-470.
- D. Butnariu, E. Resmerita, Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces, Abstr. Appl. Anal. Art. ID 84919 (2006) 1-39.
- D. Butnariu, A. N. Iusem, Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization, Applied Optimization, 40 Kluwer Academic, Dordrecht 2000.
- L.C. Ceng, J.C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math. 214 (2008) 186-201. https://doi.org/10.1016/j.cam.2007.02.022
- Y. Censor, A. Lent, An iterative row-action method for interval convex programming, J. Optim. Theory Appl. 34 (1981) 321-353. https://doi.org/10.1007/BF00934676
- O. Chadli, N.C. Wong, J.C. Yao, Equilibrium problems with applications to eigenvalue problems, J. Optim. Theory Appl. 117 (2003) 245-266. https://doi.org/10.1023/A:1023627606067
- O. Chadli, S. Schaible, J.C. Yao, Regularized equilibrium problems with an application to noncoercive hemivariational inequalities, J. Optim. Theory Appl. 121 (2004) 571-596. https://doi.org/10.1023/B:JOTA.0000037604.96151.26
- J. B. Hiriart-Urruty, C. Lemarechal, Grundlehren der mathematischen Wissenschaften, in: Convex Analysis and Minimization Algorithms II, 306, Springer-Verlag, (1993).
- G. Kassay, S. Reich, S. Sabach, Iterative methods for solving systems of variational inequalities in re exive Banach spaces, SIAM J. Optim. 21 (2011) 1319-1344. https://doi.org/10.1137/110820002
- F. Kohsaka, W. Takahashi, Proximal point algorithms with Bregman functions in Banach spaces, J. Nonlinear Convex Anal. 6 (2005) 505-523.
- W. Kumam, U. Witthayaratb, P. Kumam, S. Suantai, K. Wattanawitoon, Convergence theorem for equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces, Optimization 65 (2016) 265-280.
- I.V. Konnov, S. Schaible, J.C. Yao, Combined relaxation method for mixed equilibrium problems, J. Optim. Theory Appl. 126 (2005) 309-322. https://doi.org/10.1007/s10957-005-4716-0
- V. Martin-Marquez, S. Reich, S. Sabach, Iterative methods for approximating fixed points of Bregman nonexpansive operators, Discrete Contin. Dyn. Syst. Ser. S. 6 (2013) 1043-1063.
- J. J. Moreau, Sur la fonction polaire dune fonction semi-continue suprieurement [On the polar function of a semi-continuous function superiorly], C. R. Acad. Sci. Paris. 258 (1964) 1128-1130.
- J. W. Peng, J. C. Yao, Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Math. Comp. Model. 49 (2009) 1816-1828. https://doi.org/10.1016/j.mcm.2008.11.014
- R. P. Phelps, Convex Functions, Monotone Operators, and Differentiability, second ed., in: Lecture Notes in Mathematics, vol. 1364, Springer Verlag, Berlin, 1993.
- S. Reich, A weak convergence theorem for the alternating method with Bregman distances, in: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, New York, (1996) 313-318.
- S. Reich, S. Sabach, A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces, J. Nonlinear Convex Anal. 10 (2009) 471-485.
- S. Reich, S. Sabach, Existence and approximation of fixed points of Bregmanfirmly nonexpansive mappings in reflexive Banach spaces. In: Fixed-Point Algo-rithms for Inverse Problems in Science and Engineering, Optimization and Its Applications, 49 (2011) 301-316.
- S. Reich, S. Sabach, Two strong convergence theorems for a proximal method in reflexive Banach spaces, Numer. Funct. Anal. Optim. 31 (2010) 22-44. https://doi.org/10.1080/01630560903499852
- R. T. Rockafellar, Level sets and continuity of conjugate convex functions, Trans. Amer. Math. Soc. 123 (1966) 46-63. https://doi.org/10.1090/S0002-9947-1966-0192318-X
- S. Suantai, Y. J. Cho, P. Cholamjiak, Halperns iteration for Bregman strongly nonexpansive mappings in reflexive Banach spaces, Comput. Math. Appl. 64 (2012) 489-499. https://doi.org/10.1016/j.camwa.2011.12.026
- H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl. 116 (2003) 659-678. https://doi.org/10.1023/A:1023073621589
- Y. Yao, M. Aslam Noor, S. Zainab, Y. C. Liou, Mixed equilibrium problems and optimization problems J. Math. Anal. Appl. 354 (2009) 319-329 . https://doi.org/10.1016/j.jmaa.2008.12.055
- C. Zalinescu, Convex analysis in general vector spaces, World Scientific, River Edge, (2002).
- H. Zegeye, Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces, Filomat. 7 (2014) 1525-1536.