Geodesic
Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces
Klin-eam, Chakkrid1 ; Kaskasem, Prondanai2 ; Suantai, Suthep3
1 Department of Mathematics, Faculty of Science, Naresuan University, , Thailand., Phitsanulok, 65000, Thailand;Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand
2 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
3 Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 7, p. 4963-4975.

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

We introduce a hybrid method for finding a common element of the set of solutions of an equilibrium problem defined on the dual space of a Banach space and the set of common fixed points of a family of generalized nonexpansive mappings and prove strong convergence theorems by using the new hybrid method. Using our main results, we obtain some new strong convergence theorems for finding a solution of an equilibrium problem and a fixed point of a family of generalized nonexpansive mappings in a Banach space.
DOI : 10.22436/jnsa.009.07.01
Classification : 47J25, 47H05, 47H10
Keywords: Hybrid method, generalized nonexpansive mapping, NST-condition, equilibrium problem, fixed point problem, Banach space.

Klin-eam, Chakkrid 1 ; Kaskasem, Prondanai 2 ; Suantai, Suthep 3

1 Department of Mathematics, Faculty of Science, Naresuan University, , Thailand., Phitsanulok, 65000, Thailand;Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand
2 Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
3 Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand 
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Klin-eam, Chakkrid; Kaskasem, Prondanai; Suantai, Suthep. Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 7, p. 4963-4975. doi : 10.22436/jnsa.009.07.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.07.01/

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

[2] Combettes, P. L.; Hirstoaga, S. A. Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., Volume 6 (2005), pp. 117-136

[3] Ibaraki, T.; Takahashi, W. A new projection and convergence theorems for the projections in Banach spaces, J. Approx. Theory, Volume 149 (2007), pp. 1-14

[4] Kamimura, S.; Takahashi, W. Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim., Volume 13 (2002), pp. 938-945

[5] Kohsaka, F.; Takahashi, W. Generalized nonexpansive retractions and a proximal-type algorithm in Banach spaces, J. Nonlinear Convex Anal., Volume 8 (2007), pp. 197-209

[6] Mann, W. R. Mean value methods in iteration, Proc. Amer. Math. Soc., Volume 4 (1953), pp. 506-510

[7] Nakajo, K.; Shimoji, K.; Takahashi, W. Strong convergence to common fixed points of families of nonexpansive mappings in Banach spaces, J. Nonlinear Convex Anal., Volume 6 (2007), pp. 11-34

[8] Nakajo, K.; Takahashi, W. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl., Volume 279 (2003), pp. 372-379

[9] Reich, S. Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., Volume 67 (1979), pp. 247-276

[10] Takahashi, W. Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publ., Yokohama, 2000

[11] Takahashi, W.; Takeuchi, Y.; Kubota, R. Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., Volume 341 (2008), pp. 276-286

[12] Takahashi, W.; Zembayashi, K. A strong convergence theorem for the equilibrium problem with a bifunction defined on the dual space of a Banach space, Fixed point theory and its applications, Yokohama Publ., Yokohama, Volume 197--209 (2008)

[13] Zălinescu, C. On uniformly convex functions, J. Math. Anal. Appl., Volume 95 (1983), pp. 344-374

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