Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense

We provide a new two-step iteration scheme of mixed type for two asymptotically nonexpansive self mappings in the intermediate sense and two asymptotically nonexpansive non-self mappings in the interme- diate sense and establish some strong and weak convergence theorems for mentioned scheme and mappings in uniformly convex Banach spaces. Our results extend and generalize the corresponding results of Chidume et al. [C. E. Chidume, E. U. Ofoedu, H. Zegeye, J. Math. Anal. Appl., 280 (2003), 364–374] and [C. E. Chidume, N. Shahzad, H. Zegeye, Numer. Funct. Anal. Optim., 25 (2004), 239–257], Guo et al. [W. Guo, W. Guo, Appl. Math. Lett., 24 (2011), 2181–2185] and [W. Guo, Y. J. Cho, W. Guo, Fixed Point Theory Appl., 2012 (2012), 15 pages], Saluja [G. S. Saluja, J. Indian Math. Soc. (N.S.), 81 (2014), 369–385], Schu [J. Schu, Bull. Austral. Math. Soc., 43 (1991), 153–159], Tan and Xu [K. K. Tan, H. K. Xu, J. Math. Anal. Appl., 178 (1993), 301–308], Wang [L. Wang, J. Math. Anal. Appl., 323 (2006), 550–557], Wei and Guo [S. I. Wei, W. Guo, Commun. Math. Res., 31 (2015), 149–160] and [S. Wei, W. Guo, J. Math. Study, 48 (2015), 256–264].