Finite point compactifications of (ℕ, +)

Communicated by M. W. Mislove     

Fixed point Ishikawa iterations

We first establish sufficient conditions on the coefficients of the Ishikawa iteration process to guarantee that, if the Ishikawa iterates of a continuous selfmap T, of the unit interval, converge, then they converge to a fixed point of T. Second we obtain sufficient conditions to guarantee that the iterations converge.     

Fixed point theories and dependent choice

In this paper we establish the proof-theoretic equivalence of (i) and , (ii) and , and (iii) and . Received: 18 March 1997     

Fixed point theorems for fuzzy mappings

This paper presents some new fixed point theorems for fuzzy mappings. The results given in this paper improve and extend some recent results.     

Fixed point theorems for fuzzy numbers

In this paper we study the problem of the existence of fixed points for fuzzy maps. We first define uniform structures on sets of fuzzy subsets and describe the ‘closed convergence’ and ‘myope convergence’ structures which have properties close to the corresponding traditional ones. We then give two ways in order to obtain fixed point results. We finally give applications of these results, particularly to fuzzy Markov processes.     

Fixed point results on metric-type spaces

In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

Fixed point sets of fiber-preserving maps

Let be a fiber bundle where E, B and Y are connected finite polyhedra. Let be a fiber-preserving map and a closed, locally contractible subset. We present necessary and sufficient conditions for A and its subsets to be the fixed point sets of maps fiber homotopic to f. The necessary conditions correspond to those introduced by Schirmer in 1990 but, in the fiber-preserving setting, homotopies are fiberpreserving. Those conditions are shown to be sufficient in the presence of additional hypotheses on the bundle and on the map f. The hypotheses can be weakened in the case that f is fiber homotopic to the identity.     

Fixed point sets through iteration schemes

We introduce the notion of a general fixed point iteration scheme to unify various fixed point iterations in the literatures, and extend the concept of virtual stability of a selfmap to an iteration scheme to obtain a connection, through an explicit retraction, between the convergence set of the scheme and its fixed point set. Moreover, we illustrate how to apply our results to obtain a new criterion for contractibility of the fixed point set of a certain quasi-nonexpansive selfmap.     

Fixed point theorems for discontinuous mapping

We prove a generalization of Brouwer's famous fixed point theorem to discontinuous maps. The main result shows that for discontinuous functions on a compact convex domainX one can always find a pointx X such that x–f(x) is less than a certain measure of discontinuity. Applications to artificial neural nets, economic equilibria and analysis are given.     

Fixed point theorems in metric spaces

In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120).     

Fixed point theorems for convex sets

A conjecture of the author is verified by setting up a fundamental fixed point theorem so that some earlier results are unified and strengthened. Supported by National Foundation of Natural Science.     

Fixed point theorems in uniform spaces

Fixed point theorems in a Hausdorff uniform space are proved by considering a contractive type condition for a triplet of mappings.     

Fixed point properties in Hardy spaces

We prove that the Hardy space H¹ on the unit disc of C has the weak^∗ fixed point property for left reversible semigroups.     

Fixed point theorems for precomplete numberings

In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. We discuss various generalizations of this result. Among other things, we show that Arslanov's completeness criterion also holds for every precomplete numbering, and we discuss the relation with Visser's ADN theorem, as well as the uniformity or nonuniformity of the various fixed point theorems. Finally, we base numberings on partial combinatory algebras and prove a generalization of Ershov's theorem in this context.