A parallel iterative method for a finite family of Bregman strongly nonexpansive mappings in reflexive Banach spaces

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참고문헌 (49)

1. Y. I. Alber, "Metric and generalized projection operators in Banach spaces: properties and applications, in Theory and applications of nonlinear operators of accretive and monotone type", Lecture Notes in Pure and Appl. Math., 178, pp.15~50 (1996)
2. A. Ambrosetti, "A primer of nonlinear analysis, Cambridge Studies in Advanced Mathematics, 34" (1993), Cambridge University Press
3. H. H. Bauschke, "Bregman monotone optimization algorithms", SIAM J. Control Optim, 42(2), pp.596~636 (2003)[DOI]
4. H. H. Bauschke, "Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces", Commun. Contemp. Math, 3(4), pp.615~647 (2001)[DOI]
5. E. Blum, "From optimization and variational inequalities to equilibrium problems", Math. Student, 63(1-4), pp.123~145 (1994)
6. J. F. Bonnans, "Perturbation analysis of optimization problems, Springer Series in Operations Research" (2000), Springer-Verlag
7. F. E. Browder, "Existence and approximation of solutions of nonlinear variational in-equalities", Proc. Nat. Acad. Sci. U. S. A, 56, pp.1080~1086 (1966)[DOI]
8. D. Butnariu, "Totally convex functions for xed points computation and innite dimensional optimization, Applied Optimization, 40" (2000), Kluwer Academic Publishers
9. D. Butnariu, "A proximal-projection method for nding zeros of set-valued operators", SIAM J. Control Optim, 47(4), pp.2096~2136 (2008)[DOI]
10. D. Butnariu, "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces", Abstr. Appl. Anal, 2006, pp.39~ (2006)[DOI]
11. L. -C. Ceng, "A hybrid iterative scheme for mixed equilibrium problems and xed point problems", J. Comput. Appl. Math, 214(1), pp.186~201 (2008)[DOI]
12. Y. Censor, "An iterative row-action method for interval convex program-ming", J. Optim. Theory Appl, 34(3), pp.321~353 (1981)[DOI]
13. Y. Censor, "Iterations of paracontractions and rmly nonexpansive operators with applications to feasibility and optimization", Optimization, 37(4), pp.323~339 (1996)[DOI]
14. C. E. Chidume, "A Krasnoselskii type algorithm for ap-proximating solutions of variational inequality problems and convex feasibility problems", J. Nonlinear Var. Anal, 2, pp.203~218 (2018)
15. I. Cioranescu, "Geometry of Banach spaces, duality mappings and nonlinear problems, Mathematics and its Applications, 62" (1990), Kluwer Academic Publishers Group
16. V. Darvish, "Strong convergence theorem for a system of generalized mixed equilib-rium problems and nite family of Bregman nonexpansive mappings in Banach spaces", Opsearch, 53(3), pp.584~603 (2016)[DOI]
17. L. L. Duan, "Construction techniques of projec-tion sets in hybrid methods for innite weakly relatively nonexpansive mappings with applications", J. Nonlinear Funct. Anal, 2019 (2019)
18. G. Z. Eskandani, "A strong convergence theorem for Bregman quasi-noexpansive mappings with applications", Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM, 113(2), pp.353~366 (2019)[DOI]
19. B. Halpern, "Fixed points of nonexpanding maps", Bull. Amer. Math. Soc, 73, pp.957~961 (1967)[DOI]
20. G. Kassay, "Iterative methods for solving systems of variational inequalities in reexive Banach spaces", SIAM J. Optim, 21(4), pp.1319~1344 (2011)[DOI]
21. J. K. Kim, "Strong convergence theorems by hybrid projection methods for equilibrium problems and xed point problems of the asymptotically quasi--nonexpansive mappings", Fixed Point Theory Appl, 2011, pp.15~ (2011)[DOI]
22. J. K. Kim, "Convergence theorems of iterative sequences for generalized equilibrium prob-lems involving strictly pseudocontractive mappings in Hilbert spaces", J. Comput. Anal. Appl, 18(3), pp.454~471 (2015)
23. J. K. Kim, "An iteration method for common solution of a system of equilibrium problems in Hilbert spaces", Fixed Point Theory Appl., 2011, pp.15~ (2011)[DOI]
24. J. K. Kim, "A new iterative method for the set of solutions of equilibrium problems and of operator equations with inverse-strongly monotone map-pings", Abstr. Appl. Anal., 2014, pp.8~ (2014)[DOI]
25. J. K. Kim, "A new iterative algorithm of pseudomonotone mappings for equilibrium problems in Hilbert spaces", J. Inequal. Appl, 2013(128), pp.16~ (2013)[DOI]
26. F. Kohsaka, "Proximal point algorithms with Bregman functions in Banach spaces", J. Nonlinear Convex Anal, 6(3), pp.505~523 (2005)
27. P. -E. Mainge, "Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization", Set-Valued Anal, 16(7-8), pp.899~912 (2008)[DOI]
28. V. Martn-Marquez, "Bregman strongly nonexpansive operators in reexive Banach spaces", J. Math. Anal. Appl, 400(2), pp.597~614 (2013)[DOI]
29. J. -J. Moreau, "Sur la fonction polaire d'une fonction semi-continue superieurement", C. R. Acad. Sci. Paris, 258, pp.1128~1130 (1964)
30. E. Naraghirad, "Bregman weak relatively nonexpansive mappings in Ba-nach spaces", Fixed Point Theory Appl, 2013(141), pp.43~ (2013)[DOI]
31. S. Reich, "Review of Geometry of Banach spaces, duality mappings and nonlinear problems by Ioana Cioranescu", Bull. Amer. Math. Soc, 26, pp.367~370 (1992)[DOI]
32. 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", Lecture Notes in Pure and Appl. Math.,, 178, pp.313~318 (1996), Dekker
33. S. Reich, "A strong convergence theorem for a proximal-type algorithm in reexive Banach spaces", J. Nonlinear Convex Anal, 10(3), pp.471~485 (2009)
34. S. Reich, "Two strong convergence theorems for a proximal method in reexive Banach spaces", Numer. Funct. Anal. Optim, 31(1-3), pp.22~44 (2010)[DOI]
35. S. Reich, "Two strong convergence theorems for Bregman strongly nonexpansive operators in reexive Banach spaces", Nonlinear Anal, 73(1), pp.122~135 (2010)[DOI]
36. S. Reich, "Existence and approximation of xed points of Bregman rmly nonexpansive mappings in reexive Banach spaces, in Fixed-point algorithms for inverse problems in science and engineering", Springer Optim. Appl.,, 49, pp.301~316 (2011), Springer[DOI]
37. S. Reich, "A projection method for solving nonlinear problems in reexive Banach spaces", J. Fixed Point Theory Appl, 9(1), pp.101~116 (2011)[DOI]
38. S. Reich, "Three strong convergence theorems regarding iterative methods for solving equi-librium problems in reexive Banach spaces, in Optimization theory and related topics", Contemp. Math., 568, pp.225~240 (2012)[DOI]
39. E. Resmerita, "On total convexity, Bregman projections and stability in Banach spaces", J. Convex Anal, 11(1), pp.1~16 (2004)
40. R. T. Rockafellar, "Level sets and continuity of conjugate convex functions", Trans. Amer. Math. Soc, 123, pp.46~63 (1966)[DOI]
41. S. Suantai, "Halpern's iteration for Bregman strongly nonexpansive mappings in reexive Banach spaces", Comput. Math. Appl, 64(4), pp.489~499 (2012)[DOI]
42. W. Takahashi, "Weak convergence theorems for nonexpansive mappings and monotone mappings", J. Optim. Theory Appl, 118(2), pp.417~428 (2003)[DOI]
43. T. M. Tuyen, "Parallel iterative methods for Bregman strongly nonexpansive operators in reexive Banach spaces", J. Fixed Point Theory Appl, 19(3), pp.1695~1710 (2017)[DOI]
44. T. M. Tuyen, "Parallel iterative methods for solving systems of generalized mixed equilibrium problems in reexive Banach spaces", Optimization, 66(4), pp.623~639 (2017)[DOI]
45. A. Y. Wang, "A simple hybrid Bregman projection algorithms for a family of countable Bregman quasi-strict pseudo-contractions", Nonlinear Funct. Anal. Appl, 22(5), pp.1001~1011 (2017)
46. H. -K. Xu, "Strong convergence of an iterative method for nonexpansive and accretive operators", J. Math. Anal. Appl, 314(2), pp.631~643 (2006)[DOI]
47. C. Zalinescu, "Convex analysis in general vector spaces" (2002), World Scientic Publishing Co., Inc
48. H. Zegeye, "Convergence theorems for Bregman strongly nonexpansive mappings in re-exive Banach spaces", Filomat, 28(7), pp.1525~1536 (2014)[DOI]
49. J. Zhao, "Strong convergence for Bregman relatively nonexpansive mapping in reexive Banach spaces and applications", Nonlinear Funct. Anal. Appl, 20(3), pp.365~379 (2015)

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