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 Waterfall model has dominated software development for many years, but iteration of processes is catching in. There is now a number of well-established iterative development process models that can be classified according to the levels where iteration is applied. Iteration can improve validation and verification by allowing earlier quality feedback. Moreover, there seems to be a secret marr...

background: chlorophenols are classified as priority toxic pollutants. these acidic organic compounds present a serious potential hazard for human health and aquatic life. chlorophenols accumulate in water, soil and air due to high stability, and impart an unpleasant taste and odor to drinking water and can exert negative effects on different biological processes. among the different methods of...

We introduce iteration in process algebra by means of (the binary version of) Kleene's star operator: x y is the process that chooses between x and y, and upon termination of x has this choice again. It is proved that adding respectively interleaving, communication and abstraction operators increases expressivity up to the regular processes. However, if the distinction between (successful) term...

We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution and avoiding short positions. In this paper, we consider the Bregman iteration method to solve the related constrained optimization problem. We propose an iterative algorithm based on a...

In this paper we establish an estimate for the rate of convergence of the Krasnosel’skǐı–Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon–Bruck conjecture [3] on the asymptotic regularity of this iteration. The proof proceeds by establishing a connection between these iterates and a stochastic process involving sums of non-homogeneous Bernoull...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand Abstract We prove a convergence theorem of the Mann iteration scheme for a uniformly L-Lipschitzian asymptotically demicontractive mapping in a CAT(κ ) space with κ > 0. We also obtain a convergence theorem of the Ishikawa iteration scheme for a uniformly L-Lipsc...

In this paper, we examine the stability of KirkIshikawa and Kirk-Mann iteration processes for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space. To the best of our knowledge, apart from the results of Olatinwo [19], stability of fixed point iteration processes has not been investigated in uniformly convex Banach space. Our results generalize, extend and improve some...