Geodesic
Strong convergence theorems for mixed equilibrium problems and uniformly Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces
Jantakarn, Kittisak 1 ; Kaewcharoen, Anchalee 1
1 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 6, p. 349-362.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The purpose of this paper is to suggest a new algorithm for finding a common solution of a mixed equilibrium problem and a common fixed point of uniformly Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces. The strong convergence theorems under suitable control conditions are proven.
DOI : 10.22436/jnsa.012.06.02
Classification : 47H09, 47H10
Keywords: Mixed equilibrium problems, Bregman totally quasi-asymptotically nonexpansive mappings, reflexive Banach spaces

Jantakarn, Kittisak  1 ; Kaewcharoen, Anchalee  1

1 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand 
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Jantakarn, Kittisak ; Kaewcharoen, Anchalee . Strong convergence theorems for mixed equilibrium problems and uniformly Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 6, p. 349-362. doi : 10.22436/jnsa.012.06.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.06.02/

[1] Blum, E.; Oettli, W. From optimization and variational inequalities to equilibrium problems, Math. Student, Volume 63 (1994), pp. 123-145

[2] Brégman, 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., Volume 7 (1967), pp. 200-217 | DOI

[3] Butnariu, D.; Iusem, A. N. Totally convex functions for fixed points computation and infinite dimensional optimization, Academic press, Dordrecht, 2012 | DOI

[4] Butnariu, D.; Resmerita, E. Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces, Abstr. Appl. Anal., Volume 2006 (2006), pp. 1-39 | Zbl

[5] Ceng, L.-C.; Yao, J.-C. A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math., Volume 214 (2008), pp. 186-201 | DOI

[6] Censor, Y.; A. Lent An iterative row-action method for interval convex programming, J. Optim. Theory Appl., Volume 34 (1981), pp. 321-353 | DOI | Zbl

[7] Chang, S. S.; Wang, L.; Wang, X. R.; C. K. Chan Strong convergence theorems for Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces, Appl. Math. Comput., Volume 228 (2014), pp. 38-48 | DOI | Zbl

[8] Darvish, V. A new algorithm for mixed equilibrium problem and Bregman strongly nonexpansive mapping in Banach spaces, arXiv, Volume 2015 (2015), pp. 1-20

[9] Huang, Y. Y.; Jeng, J. C.; Kuo, T. C.; Hong, C. C. Fixed point and weak convergence theorems for point-dependent \(\lambda\)-hybrid mappings in Banac spaces, Fixed Point Theory Appl., Volume 2011 (2011), pp. 1-15 | DOI

[10] Kassay, G.; Reich, S.; Sabach, S. Iterative methods for solving systems of variational inequalities in reflexive Banach spaces, SIAM. J. Optim., Volume 21 (2011), pp. 1319-1344 | Zbl | DOI

[11] Nilsrakoo, W.; Saejung, S. Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces, Appl. Math. Comput., Volume 217 (2011), pp. 6577-6586 | DOI

[12] Reich, S.; Sabach, S. Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces, Nonlinear Anal., Volume 73 (2010), pp. 122-135 | Zbl | DOI

[13] Reich, S.; Sabach, S. Two strong convergence theorems for a proximal method in reflexive Banach spaces, Numer. Funct. Anal. Optim., Volume 31 (2010), pp. 22-44 | Zbl | DOI

[14] Reich, S.; Sabach, S. Existence and approximation of fixed points of Bregman firmly nonexpansive mappings in reflexive Banach spaces, in: Fixed-Point Algorithms for Inverse Problemsin Science and Engineering, Academic Press, Volume 2011 (2011), pp. 301-316 | Zbl | DOI

[15] Suantai, S.; Cho, Y. J.; Cholamjiak, P. Halpern’s iteration for Bregman strongly nonexpansive mappings in reflexive Banach spaces, Comput. Math. Appl., Volume 64 (2012), pp. 489-499 | DOI

[16] Wang, S. H.; Kang, S. M. Strong convergence iterative algorithms for equilibrium problems and fixed point problems in Banach spaces, Abstr. Appl. Anal., Volume 2013 (2013), pp. 1-9

[17] Zhu, S.; Huang, J. H. Strong convergence theorems for equilibrium problem and Bregman totally quasi-asymptotically nonexpansive mapping in Banach spaces, Acta Math. Sci. Ser. B (Engl. Ed.), Volume 36 (2016), pp. 1433-1444 | DOI | Zbl

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