-Stability of Picard Iteration in Metric Spaces
نویسندگان
چکیده
منابع مشابه
T-Stability of Picard Iteration in Metric Spaces
Let X, d be a complete metric space and T a self-map of X. Let xn 1 f T, xn be some iteration procedure. Suppose that F T , the fixed point set of T , is nonempty and that xn converges to a point q ∈ F T . Let {yn} ⊂ X and define n d yn 1, f T, yn . If lim n 0 implies that limyn q, then the iteration procedure xn 1 f T, xn is said to be T -stable. Without loss of generality, we may assume that ...
متن کاملOn T-Stability of Picard Iteration in Cone Metric Spaces
i P is closed, nonempty, and P / {0}, ii a, b ∈ R, a, b ≥ 0, and x, y ∈ P imply that ax by ∈ P, iii x ∈ P and −x ∈ P imply that x 0. The space E can be partially ordered by the cone P ⊂ E; by defining, x ≤ y if and only if y − x ∈ P . Also, we write x y if y − x ∈ int P , where int P denotes the interior of P . A cone P is called normal if there exists a constant K > 0 such that 0 ≤ x ≤ y impli...
متن کاملStable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration
This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and extended altering-distance functions, the last ones being piecewise continuous. The conditions for themaps to be contractive for the achievement o...
متن کاملiteration for ( quasi ) minimizers on metric spaces
We study regularity properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces. We adapt the Moser iteration technique to this setting and show that it can be applied without an underlying differential equation. However, we have been able to run the Moser iteration fully only for minimizers. We prove Caccioppoli inequalities and local boundedness properties for quasisuba...
متن کاملA Picard Iteration Based Integrator
converge to a unique solution of the IVP up to the boundary of U [1]. In general, φn may converge slowly to the exact solution. The Picard iteration based integrator described in this paper has three main advantages. The the integrator has arbitrary order, is time adaptive, and has dense output. Dense output refers to the integrator being able to take time steps of variable length without havin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2008
ISSN: 1687-1812
DOI: 10.1155/2008/418971