the purpose of this paper is to study the convergence and the almost sure t-stability of the modied sp-type random iterative algorithm in a separable banach spaces. the bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure t-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. our resu...

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...

Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1, T2, . . . , TN : K −→ E be N asymptotically nonexpansive nonself mappings with sequences {r n} such that ∑∞ n=1 r n < ∞, for all 1 ≤ i ≤ N and F = ∩i=1F (Ti) 6= φ. Let {α n}, {β n} and {γ n} are sequences in [0, 1] with α n + β i n + γ i n = 1 for all i =...

The study of fixed points for multivalued contractions and nonexpansive maps using the Hausdorff metric was initiated by Markin [17]. Later, an interesting and rich fixed point theory for such maps has been developed. The theory of multivalued maps has applications in control theory, convex optimization, differential inclusions, and economics (see, e.g., [3, 8, 16, 22]). The theory of multivalu...

In this paper, we obtain the strong convergence of a Halpern type iterative scheme to a fixed point of nonself nonexpansive mapping in Banach spaces. Our results improve and extend the corresponding results of Jung [6], Song [12,13], Aoyama [2]. Mathematics Subject Classification: 47H09, 47J25

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E , which is also a nonexpansive retract of E with nonexpansive retraction P . Let {Ti : i ∈ I } be N nonself asymptotically nonexpansive mappings from K to E such that F = {x ∈ K : Ti x = x, i ∈ I } 6= φ, where I = {1, 2, . . . , N }. From arbitrary x0 ∈ K , {xn} is defined by xn = P((1− αn)xn−1 + αnTn(PT...

and Applied Analysis 3 It is easy to see that a quasi-nonexpansive mapping is an asymptotically quasi-nonexpansive mapping with the sequence {1}. T is said to be asymptotically nonexpansive in the intermediate sense if and only if it is continuous, and the following inequality holds: lim sup n→∞ sup x,y∈C (∥ ∥Tx − Tny∥∥ − ∥∥x − y∥∥) ≤ 0. 2.6 T is said to be asymptotically quasi-nonexpansive in ...

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotical...