A generalization of Halpern’s iteration is investigated on a compact convex subset of a smooth Banach space. The modified iteration process consists of a combination of a viscosity term, an external sequence, and a continuous nondecreasing function of a distance of points of an external sequence, which is not necessarily related to the solution of Halpern’s iteration, a contractive mapping, and...

The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...

REPORTRAPPORT Basic process algebra with iteration: completeness of its equational axioms Abstract Bergstra, Bethke & Ponse BBP93] proposed an axiomatisation for Basic Process Algebra extended with (binary) iteration. In this paper, we prove that this axiomatisation is complete with respect to strong bisimulation equivalence. To obtain this result, we will set up a term rewriting system, based ...

Extreme Programming (XP) was introduced as a new process model, which has three main activities in each XP iteration cycle: new design, error-fix, and refactoring. In an empirical study on two Java systems developed using an XP-like process, we found that new design seems to dominate the development effort throughout all iteration cycles. We also found that the evolutionary trends of all three ...

In this paper, strong convergence theorems of Ishikawa type implicit iteration process with errors for a finite family of asymptotically nonexpansive in the intermediate sense and asymptotically quasi-pseudocontractive type mappings in normed linear spaces are established by using a new analytical method, which essentially improve and extend some recent results obtained by Yang [Convergence the...

In this paper, we shall establish some strong convergence results for the recently introduced Jungck-Mann iteration process of Singh et al. [18] and the newly introduced Jungck-Ishikawa iteration process in the class of non-selfmappings in an arbitrary Banach space. Our results are generalizations and extensions of those of Berinde [4], Rhoades [13, 14] as well as some other analogous ones in t...

Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the ...

We denote the set of all fixed points of T by Fix(T); for more details see []. The concept of -convergence in general metric spaces was introduced by Lim []. Kirk [] has proved the existence of fixed point of nonexpansive mappings in CAT() spaces. Kirk and Panyanak [] specialized this concept to CAT() spaces and showed that many Banach space results involving weak convergence have precise...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

Compositions of command statements, branching, iteration and recursion are primarily used in high-level programming languages to devise algorithms and obtain structured control flow. These structuring building blocks may also be instrumental for describing real-life systems in analysis and design methodologies at any complexity level. While composition and branching are incorporated into most p...