A new general composite implicit random iteration scheme with perturbed mapping is proposed and obtain necessary and sufficient conditions for strong convergence of proposed iteration scheme to random fixed point of a finite family of random nonexpansive mappings are obtained.

The aim of this article is to establish some strong convergence theorems of three-step iteration process with errors for approximating common fixed point for generalized asymptotically quasi-nonexpansive mappings and also establish a weak convergence theorem by using Opial’s [11] condition for said iteration scheme and mappings in the framework of Banach spaces. The results presented in this pa...

Abstract In this paper, we study the Ishikawa type iteration process with errors, which converges to a common fixed point of a pair of mappings in complete generalized convex metric spaces. Furthermore, we obtain the corresponding results in Banach spaces. Our result improve and generalize a recent result of Khan[S.H. Khan, Common fixed points of two quasi-contractive operators in normed spaces...

This article continues prior work of the authors on the combined a posteriori analysis for the discretization and iteration errors in the finite element approximation of linear elliptic problems to the nonlinear case. The underlying theoretical framework is again that of the Dual Weighted Residual (DWR) method for goal-oriented error control. The accuracy in the algebraic solution process can b...

We show the convergence of an implicit mean value iteration when applied to uniformly pseudocontractive maps. Remarks about other implicit mean value iterations are given.

Let E be a real Banach space, {Ti}i=1 be a finite family of continuous pseudocontractive self mappings of E and G : E → E be a mapping which is both δ -strongly accretive and λ -strictly pseudocontractive of Browder-Petryshyn type such that δ + λ 1 . We propose a new implicit iteration scheme with perturbed mapping G for the approximation of common fixed points of {Ti}i=1 . For an arbitrary ini...

The aim of this paper is to study an implicit iterative process for a finite family of T-Ciric quasi-contractive operators and also establish the strong convergence of above said iteration process using the common fixed points of a finite family of above said operators in the framework of CAT(0) spaces. Our results improve and extend some corresponding recent results from the current existing l...

Implicit methods for Hamilton–Jacobi–Bellman (HJB) partial differential equations give rise to highly nonlinear discretized algebraic equations. The classic policy iteration approach may not be efficient in many circumstances. In this article, we derive sufficient conditions to ensure convergence of a combined fixed point policy iteration scheme for the solution of discretized equations. Numeri...