We construct random iterative processes for weakly contractive and asymptotically nonexpansive random operators and study necessary conditions for the convergence of these processes. It is shown that they converge to the random fixed points of these operators in the setting of Banach spaces. We also proved that an implicit random iterative process converges to the common random fixed point of a...

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...

We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

and Applied Analysis 3 In this paper, we generalize and modify the iteration of Abbas et al. 7 from two mapping to the infinite family mappings {Ti : i ∈ N} of multivalued quasi-nonexpansive mapping in a uniformly convex Banach space. Let {Ti} be a countable family of multivalued quasi-nonexpansive mapping from a bounded and closed convex subset K of a Banach space into P K with F : ⋂∞ i 1 F Ti...

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

The purpose of this paper is to provide the new demicloseness principle– τ (weakly) demicloseness principle. We prove that if X is a Banach space with locally uniformly τ -Opial condition, where τ is a Hausdorff topology on X, C is a nonempty τ compact subset of X, and T : C → C is a asymptotically nonexpansive type mapping. If {xα} is a net in C which converges to x in the sense of τ topology ...

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...