Search results for " ITER"
showing 10 items of 79 documents
Coupled fixed point, F-invariant set and fixed point of N-order
2010
In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of $F$-invariant set. We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement some known existence results from the literature.
Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems
2016
In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we …
Common fixed points for discontinuous mappings in fuzzy metric spaces
2008
In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena.
Law of the Iterated Logarithm
2020
For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large \(n\in \mathbb{N}\) the typical behavior, or average value behavior, of sums of n random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.
Conditional Random Quantities and Iterated Conditioning in the Setting of Coherence
2013
We consider conditional random quantities (c.r.q.’s) in the setting of coherence. Given a numerical r.q. X and a non impossible event H, based on betting scheme we represent the c.r.q. X|H as the unconditional r.q. XH + μH c , where μ is the prevision assessed for X|H. We develop some elements for an algebra of c.r.q.’s, by giving a condition under which two c.r.q.’s X|H and Y|K coincide. We show that X|HK coincides with a suitable c.r.q. Y|K and we apply this representation to Bayesian updating of probabilities, by also deepening some aspects of Bayes’ formula. Then, we introduce a notion of iterated c.r.q. (X|H)|K, by analyzing its relationship with X|HK. Our notion of iterated conditiona…
Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces
2013
We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.
The symmetric boundary element method for unilateral contact problems
2008
Abstract On the basis of the boundary integral equation method, in its symmetric formulation, the frictionless unilateral contact between two elastic bodies has been studied. A boundary discretization by boundary elements leads to an algebraic formulation in the form of a linear complementarity problem. In this paper the process of contact or detachment is obtained through a step by step analysis by using generalized (weighted) quantities as the check elements: the detachment or the contact phenomenon may happen when the weighted traction or the weighted displacement is greater than the weighted cohesion or weighted minimum reference gap, respectively. The applications are performed by usin…
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
2021
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide r…
Localization and separation of solutions for Fredholm integral equations
2020
[EN] In this paper, we establish a qualitative study of nonlinear Fredholm integral equations, where we will carry out a study on the localization and separation of solutions. Moreover, we consider an efficient algorithm to approximate a solution. To do this, we study the semilocal convergence of an efficient third order iterative scheme for solving nonlinear Fredholm integral equations under mild conditions. The novelty of our work lies in the fact that this study involves first order Frechet derivative and mild conditions. A numerical example involving nonlinear Fredholm integral equations, is solved to show the domains of existence and uniqueness of solutions. The applicability of the it…
Missing Value Estimation for Microarray Data by Bayesian Principal Component Analysis and Iterative Local Least Squares
2013
Published version of an article from the journal: Mathematical Problems in Engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2013/162938 Missing values are prevalent in microarray data, they course negative influence on downstream microarray analyses, and thus they should be estimated from known values. We propose a BPCA-iLLS method, which is an integration of two commonly used missing value estimation methods-Bayesian principal component analysis (BPCA) and local least squares (LLS). The inferior row-average procedure in LLS is replaced with BPCA, and the least squares method is put into an iterative framework. Comparative result shows that the proposed method has obtaine…