Related papers: On computing fixpoints in well-structured regular …

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

We prove a fixpoint theorem for contractions on Cauchy-complete quantale-enriched categories. It holds for any quantale whose underlying lattice is continuous, and applies to contractions whose control function is sequentially…

Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…

We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…

We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.

This paper provides an overview of Lawvere's Fixed-Point Theorem in category theory and aims to detail the universal framework underlying self-reference and recursive structures. First, we rigorously define fundamental concepts - such as…

We establish conditions under which a continuous time reservoir computer, such as a leaky integrator echo state network, admits a generalised synchronisation $f$ between between the source dynamics and reservoir dynamics. We show that…

We present a class of iterative fully distributed fixed point methods to solve a system of linear equations, such that each agent in the network holds one of the equations of the system. Under a generic directed, strongly connected network,…

In this paper we prove FG-coupled fixed point theorems for different contractive mappings and generalized quasi- contractive mappings in partially ordered complete metric spaces. We prove the existence of FG-coupled fixed points of…

In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et…

With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…

We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.

This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…

We give a new proof of the result that if f and g are transcendental entire functions, then the composite function f(g) has infinitely many fixed points. The method yields a number of generalization of this result. In particular, it extends…

We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a…

In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…