A new iteration scheme for a hybrid pair of generalized nonexpansive mappings
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Suzuki T: Fixed point theorems and convergence theorems for some generalized nonexpansive mappings. J. Math. Anal. Appl. 2008, 340: 1088–1095. 10.1016/j.jmaa.2007.09.023
Picard E: Mémoire sur la théorie des équations aux dérivées partielles et la méthode des approximations successives. J. Math. Pures Appl. 1890, 6: 145–210.
Mann WR: Mean value methods in iterations. Proc. Am. Math. Soc. 1953, 4: 506–510. 10.1090/S0002-9939-1953-0054846-3
Ishikawa S: Fixed points by a new iteration method. Proc. Am. Math. Soc. 1974, 44: 147–150. 10.1090/S0002-9939-1974-0336469-5
Nadler SB Jr.: Multivalued contraction mappings. Pac. J. Math. 1969, 30: 475–488. 10.2140/pjm.1969.30.475
Markin JT: Continuous dependence of fixed point sets. Proc. Am. Math. Soc. 1973, 38: 545–547. 10.1090/S0002-9939-1973-0313897-4
Gorniewicz L: Topological Fixed Point Theory of Multivalued Mappings. Kluwer Academic, Dordrecht; 1999.
Lim TC: A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach spaces. Bull. Am. Math. Soc. 1974, 80: 1123–1126. 10.1090/S0002-9904-1974-13640-2
Sastry KPR, Babu GVR: Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point. Czechoslov. Math. J. 2005, 55: 817–826. 10.1007/s10587-005-0068-z
Panyanak B: Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces. Comput. Math. Appl. 2007, 54: 872–877. 10.1016/j.camwa.2007.03.012
Song Y, Wang H: Convergence of iterative algorithms for multivalued mappings in Banach spaces. Nonlinear Anal. 2009, 70: 1547–1556. 10.1016/j.na.2008.02.034
Shahzad N, Zegeye H: On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces. Nonlinear Anal. 2009, 71: 838–844. 10.1016/j.na.2008.10.112
Berinde V Lecture Notes in Mathematics 1912. In Iterative Approximation of Fixed Points. Springer, Berlin; 2007.
Sokhuma K, Kaewkhao A: Ishikawa iterative process for a pair of single-valued and multivalued nonexpansive mappings in Banach spaces. Fixed Point Theory Appl. 2010., 2010: Article ID 618767
Akkasriworn N, Sokhuma K, Chuikamwong K: Ishikawa iterative process for a pair of Suzuki generalized nonexpansive single valued and multivalued mappings in Banach spaces. Int. J. Math. Anal. 2012, 6(19):923–932.
Sokhuma K: Δ-Convergence theorems for a pair of single-valued and multivalued nonexpansive mappings in CAT(0) spaces. J. Math. Anal. 2013, 4(2):23–31.
Uddin, I, Imdad, M, Ali, J: Convergence theorems for a hybrid pair of generalized nonexpansive mappings in Banach spaces. Bull. Malays. Math. Soc. (accepted)
Sokhuma K: Convergence theorems for a pair of asymptotically and multi-valued nonexpansive mapping in Banach spaces. Int. J. Math. Anal. 2013, 7(19):927–936.
Kaewcharoen A, Panyanak B: Fixed point theorems for some generalized multivalued nonexpansive mappings. Nonlinear Anal. 2011, 74: 5578–5584. 10.1016/j.na.2011.05.042
García-Falset J, Llorens-Fuster E, Suzuki T: Fixed point theory for a class of generalized nonexpansive mappings. J. Math. Anal. Appl. 2011, 375: 185–195. 10.1016/j.jmaa.2010.08.069
Schu J: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bull. Aust. Math. Soc. 1991, 43: 153–159. 10.1017/S0004972700028884
Song Y, Cho YJ: Some notes on Ishikawa iteration for multivalued mappings. Bull. Korean Math. Soc. 2011, 48(3):575–584. 10.4134/BKMS.2011.48.3.575
Khan SH, Fukhar-ud-din H: Weak and strong convergence of a scheme with errors for two nonexpansive mappings. Nonlinear Anal. 2005, 8: 1295–1301.
Fukhar-ud-din H, Khan SH: Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications. J. Math. Anal. Appl. 2007, 328: 821–829. 10.1016/j.jmaa.2006.05.068