Strong convergence theorems for a countable family of quasi-ϕ-asymptotically nonexpansive nonself mappings

Goebel, 1990 Chidume, 2003, Strong and weak convergence theorems for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 280, 364, 10.1016/S0022-247X(03)00061-1 Alber, 1996, Metric and generalized projection operators in Banach spaces: properties and applications, 15 E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Stud 63 (1/4) (1994) 123–145. Chang, 2011, Modified Block iterative algorithm for quasi-ϕ-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces, Appl. Math. Comput., 217, 7520, 10.1016/j.amc.2011.02.060 Chang, 2010, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. TMA, 73, 2260, 10.1016/j.na.2010.06.006 Su, 2010, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal., 73, 3890, 10.1016/j.na.2010.08.021 Hukmi Kiziltunc, Seyit Temir, Convergence theorems by a new iteration process for a finite family of nonself asymptotically nonexpansive mappings with errors in Banach spaces, Comput. Math. Appl. 61 (9) (2011) 2480–2489. Isa YIldIrIm, Murat Ozdemir, A new iterative process for common fixed points of finite families of non-self-asymptotically non-expansive mappings, in: Nonlinear Analysis: Theory, Methods and Applications, vol. 71 (3–4), 1–15 August 2009, pp. 991–999. Liping Yang, Xiangsheng Xie, Weak and strong convergence theorems of three step iteration process with errors for nonself-asymptotically nonexpansive mappings, Math. Comput. Modell. 52 (5–6) (2010) 772–780. Lin Wang, Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, J. Math. Anal. Appl. 323 (1) (2006) 550–557. Lin Wang, Explicit iteration method for common fixed points of a finite family of nonself asymptotically nonexpansive mappings, Comput. Math. Appl. 53 (7) (2007) 1012–1019. Pathak, 2009, Strong and weak convergence theorems for nonself-asymptotically perturbed nonexpansive mappings, Nonlinear Anal.: Theory Meth. Appl., 70, 1929, 10.1016/j.na.2008.02.092 Sornsak Thianwan, Common fixed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space, J. Comput. Appl. Math. 224 (2) (2009) 688–695. Xiaolong Qin, Sun Young Cho, Tianze Wang, Shin Min Kang, Convergence of an implicit iterative process for asymptotically pseudocontractive nonself-mappings, Nonlinear Anal., 2011. doi:10.1016/j.na.2011.04.031. Y. Hao, S.Y. Cho, X. Qin, Some weak convergence theorems for a family of asymptotically nonexpansive nonself mappings, Fixed Point Theory Appl., 2010. Article ID 218573. Weiping Guo, Wei Guo, Weak convergence theorems for asymptotically nonexpansive nonself-mappings, Appl. Math. Lett. 24 (2011) 2181–2185. Weerayuth Nilsrakoo, Satit Sajung, Strong convergece theorems by Halpern–Mann iterations for relatively nonexpansive mappings in Banach spaces, Appl. Math. Comput. 217 (14) (2011) 6577–6586. Shih-sen Chang, H.W. Joseph Lee, Chi Kin Chan, Li Yang, Approximation theorems for total quasi-ϕ-asymptotically nonexpansive mappings with applications, Appl. Math. Comput. 218 (2011) 2921–2931. Wang, 2011, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math., 235, 2364, 10.1016/j.cam.2010.10.036 Zegeye, 2010, Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings, Appl. Math. Comput., 216, 3439, 10.1016/j.amc.2010.02.054 Chang, 2012, A modified Halpern-type iterative algorithm for totally quasi-ϕ-asymptotically nonexpansive mappings with applications, Appl. Math. Comput., 218, 6489, 10.1016/j.amc.2011.12.019