Let X be a Banach space and K a nonempty subset of X. The set K is called proximinal if for each x ∈ X, there exists an element y ∈ K such that ‖x − y‖ d x,K , where d x,K inf{‖x − z‖ : z ∈ K}. Let CB K , C K , P K , F T denote the family of nonempty closed bounded subsets, nonempty compact subsets, nonempty proximinal bounded subsets of K, and the set of fixed points, respectively. A multivalu...

In many iterative schemes, the precision of each step depends on the computational effort spent on that step. A method of specifying a suitable amount of computation at each step is described. The approach is adaptive and aimed at minimizing the overall computational cost subject to attaining a final iterate that satisfies a suitable error criterion. General and particular cost functions are co...

Interference graphs are used for performance analysis of multiprocessor interconnection networks. In order to model blocked transmissions, nodes can have three states: idle, active or blocked. The resulting steady state probability distribution has a non-product form. Macro states are introduced to calculate performance measures, and the corresponding macro state probability distribution is app...

The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The ob...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

We analyze inexact fixed point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed point iteration. Important applications are the Picard iteration and partitioned fluid structure interaction. We prove that the iteration converges irrespective of ho...

We propose a novel approach to the decomposition of large probabilistic models. The goal of our method is to avoid the evaluation of the subnetworks obtained by decomposition for all values of the state description vector, as would be necessary with a standard aggregation and decomposition approach. Instead, we propose a fixed-point iteration that requires the evaluation of the subnetwork for o...

It is well known that a fixed point iteration for solving a linear equation system converges if and only if the spectral radius of the iteration matrix is less than one. A method is presented which guarantees the Fixed Point, even if this condition is not ("spectral radius<1") fulfilled and demonstrated through calculation examples.

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...