begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as hi...

We give a strong approximation of Rosenblatt process via transport processes and we give the rate of convergence.

This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested. by Robbins and Monro [1]. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic mean).

Using the concept of CATp(0) spaces proposed by Khamsi et al. [Khamsi, M. A. and Shukri, S. A., Generalized CAT(0) spaces. Bull. Belg. Math. Soc. Simon Stevin, 24 (2017), No. 3, 417–426], we establish ∆-convergence strong convergence a perturbed variant Agarwal S-iteration process for nonexpansive mapping. Finally, from them deduce results valid α-nonexpansive mappings.

let $c$ be a nonempty closed convex subset of a real hilbert space $h$. let ${s_n}$ and ${t_n}$ be sequences of nonexpansive self-mappings of $c$, where one of them is a strongly nonexpansive sequence. k. aoyama and y. kimura introduced the iteration process $x_{n+1}=beta_nx_n+(1-beta_n)s_n(alpha_nu+(1-alpha_n)t_nx_n)$ for finding the common fixed point of ${s_n}$ and ${t_n}$, where $uin c$ is ...

The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al.[Convergence analysis of implicit iterative algorithms for asymptotically nonexpan...

In this paper we study dynamic iteration techniques for nonlinear differential equations with mixed modification of the argument. The dynamic iteration method generalizes the well known Picard iterations, improving significantly the convergence speed of the iterative process. It also have the advantage of decoupling the part containing the modified argument so the iteration steps consist in sol...

and Applied Analysis 3 Very recently, Qin et al. 16 proposed the composite Halpern type iterative scheme in a uniformly smooth Banach space as follows: x0 x, u ∈ C, zn γnxn ( 1 − γn ) Txn, yn βnxn ( 1 − βn ) Tzn, xn 1 αnu 1 − αn yn, n ≥ 0, 1.6 and showed strong convergence of the sequence {xn} generated by 1.6 under the following control conditions: i ∑∞ n 0αn ∞; ii limn→∞αn 0, limn→∞βn 0 and 0...

A mapping T : C → C is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We denote by Fix T {x ∈ C : Tx x} the set of fixed points of T . In the last ten years, many papers have been written on the approximation of fixed point for nonlinear mappings by using some iterative processes see, e.g., 1–18 . An explicit iterative process was initially introduced, in 1967, by Halpern 3 i...