Strong convergence theorems for finitely many nonexpansive mappings and applications

Hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems

“…It is very useful in establishing the convergence of iterative methods for computing a common fixed point of nonlinear mappings (see, for instance, [23,25,27]). Let l n,1 , l n,2 ..., l n, N (0, 1], n ≥ 1.…”

“…It is worth pointing out that, related iterative methods for solving fixed point problems, variational inequalities and optimization problems can be found in [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Strong convergence theorems and rate of convergence of multi-step iterative methods for continuous mappings on an arbitrary interval

“…Let W n : C C be a mapping defined by where I is the identity mapping of C and l n,i [0,1] for all i = 1, 2,..., N. Such a mapping W n is called the W-mapping generated by T 1 , T 2 ,..., T n and l n,1 , l n,2 ,..., l n,N . Many researchers have studied and applied this mapping for finding a common fixed point of nonexpansive mappings, for instance, see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

“…The W (T,N) -iteration is defined by u 1 E and 9) where N ≥ 1 and W (T,N) n is a mapping of E into itself generated by 10) where I is the identity mapping of E and l n,i [0,1] for all i = 1, 2,..., N. We call a mapping W (T,N) n as the W-mapping generated by T and l n,1 , l n,2 ,..., l n,N . Clearly W (T,1) -iteration is Mann iteration, W (T,2) -iteration is Ishikawa iteration and W (T,3) -iteration is Noor iteration.…”

New iteration algorithms for an asymptotically nonexpansive mapping

“…The asymptotically nonexpansive mappings were introduced by Goebel and Kirk [7], and they proved that if K is a nonempty bounded closed and convex subset of a uniformly convex Banach space E, then every asymptotically self-nonexpansive T on K has a fixed point. Whereafter, numerous convergence results have been proved on iterative methods for approximating fixed points of asymptotically nonexpansive mappings (e.g., Chang [5], Chidume, Li and Udomene [6], Ceng, Cubiotti and Yao [2,3], Ceng and Yao [1], Ceng, Xu and Yao [4], Lim and Xu [9], Petruşel and Yao [11,12], Song [19], Schu [13,14], Shioji and Takahashi [16,17], Tan and Xu [26], Yao and Zeng [28] and the references contained therein. In particular, Schu [14] proved the following theorems.…”