We introduce Partitioned Dependency Graphs (PDGs), an abstract framework for the speci cation and evaluation of arbitrarily nested alternating xed points. The generality of PDGs subsumes that of similarly proposed models of nested xed-point computation such as Boolean graphs, Boolean equation systems, and the propositional modal mu-calculus. Our main result is an e cient local algorithm for eva...

In this article we present a variant of the basic result of "T. Gnana. Bhaskar and V. Lakshmikanthan, Fixed point theorem in partially ordered metric spaces and applications, Nonlinear Anal. TMA, 65 (2006), 1379–1393." to …nd the coupled …xed points of multivalued mappings without mixed monotone property in cone metric space involving non-normal cones. As applications we prove the existence of ...

A signature gives rise to a language L (Var) by extending with variables x 2 Var and binding constructs x and x, corresponding to least and greatest xed points respectively. The natural denotational models for such languages are bicomplete dcpos as monotone-algebras. We prove that several approximating denotational semantics have the usual compositional semantics as their limit. These results p...

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.

We study ve extensions of the polymorphically typed lambda-calculus (system F) by type constructs intended to model xed-points of monotone operators. Building on work by H. Geuvers concerning the relation between term rewrite systems for least pre-xed-points and greatest post-xed-points of positive type schemes (i. e., non-nested positive inductive and coinductive types) and so-called retract t...

We consider a perturbed nonlinear system with a xed point that is invariant under all perturbations. Under the assumption that this xed point is locally exponentially stable for the unperturbed system we propose a method for the approximation of the robust domain of attraction, that is, the set of points that are attracted to the xed point under all time-varying perturbations taking values in a...

Given a set S of n points in IR D , D 2. Each point p 2 S is assigned a color c(p) chosen from a xed color set. The All-Nearest-Foreign-Neighbors Problem (ANFNP) is to nd for each point p 2 S its nearest foreign neighbors, i.e. the set of all points in Snfpg that are closest to p among the points in S with a color diierent from c(p). We introduce the Well Separated Color Decomposition (WSCD) wh...

We introduce Partitioned Dependency Graphs (PDGs), an abstract framework for the speciication and evaluation of arbitrarily nested alternating xed points. The generality of PDGs subsumes that of similarly proposed models of nested xed-point computation such as Boolean graphs, Boolean equation systems, and the propositional modal mu-calculus. Our main result is an eecient local algorithm for eva...

We consider the problem of computing approximations to xed points of quasilinear contraction mappings ? deened on the space of continuous functions of d variables. Our main emphasis is on large d. Examples of such mappings include the Bellman operator from the theory of dynamic programming. This paper proves that there exist deterministic algorithms for computing approximations to xed points fo...