134 research outputs found

    Convergence theorems for common fixed point of the family of nonself and nonexpansive mappings in real Banach spaces

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    In this paper, we construct cyclic-Mann type of iterative method for approximating a common fixed point of the finite family of nonself and nonexpansive mappings satisfying inward condition on a non-empty, closed and convex subset of a real uniformly convex Banach space . We also construct the averaging algorithm to the class of nonexpansive mappings in 2-uniformly smooth Banach space. We prove weak and strong convergence results for the iterative method. The results of this work extend results in the literature

    Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings

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    In this work we prove a new strong convergence result of the regularized successive approximation method given by yn+1 = qnz0 + (1 − qn)T n yn, n = 1, 2, ..., where limn→∞ qn = 0 and X∞ n=1 qn = ∞, for T a total asymptotically nonexpansive mapping, i.e., T is such that kT nx − T n yk ≤ kx − yk + k (1) n φ(kx − yk) + k (2) n , where k 1 n and k 2 n are real null convergent sequences and φ : R+ → R+ is continuous and such that φ(0) = 0 and limt→∞ φ(t) t ≤ C for a certain constant C > 0. Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self- and nonself-mappings

    Convergence theorems for nonself asymptotically nonexpansive mappings

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    In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a uniformly convex Banach space. This will improve and generalize the corresponding results in the existing literature. Finally, we will state that our theorems can be generalized to the case of finitely many mappings

    Strong convergence of averaging iterations of nonexpansive nonself-mappings

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    AbstractLet C be a closed convex subset of Hilbert space H, T a nonexpansive nonself-mapping from C into H, and x0,x,y0,y elements of C. In this paper, we study the convergence of the two sequences generated by xn+1=1n+1∑j=0nαnx+(1−αn)(PT)jxnforn=0,1,2,…,yn+1=1n+1∑j=0nPαny+(1−αn)(TP)jynforn=0,1,2,…, where {αn} is a real sequence such that 0⩽αn⩽1, and P is the metric projection from H onto C

    Some Weak Convergence Theorems for a Family of Asymptotically Nonexpansive Nonself Mappings

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    A one-step iteration with errors is considered for a family of asymptotically nonexpansive nonself mappings. Weak convergence of the purposed iteration is obtained in a Banach space
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