On a fixed-point theorem of Banach-type for uniform spaces
On a Freedman's problem
On a game of Sierpiński
On a generalization of a Greguš fixed point theorem
Let be a closed convex subset of a complete convex metric space . In this paper a class of selfmappings on , which satisfy the nonexpansive type condition below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
On a generalization of Abelian sequential groups
Let (G,τ) be a Hausdorff Abelian topological group. It is called an s-group (resp. a bs-group) if there is a set S of sequences in G such that τ is the finest Hausdorff (resp. precompact) group topology on G in which every sequence of S converges to zero. Characterizations of Abelian s- and bs-groups are given. If (G,τ) is a maximally almost periodic (MAP) Abelian s-group, then its Pontryagin dual group is a dense -closed subgroup of the compact group , where is the group G with the discrete...
On a generalization of the Conley index
In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain some of...
On a modified game of Sierpiński
On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents
On a problem of Freudenthal's
On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces
Let be a uniformly convex Banach space, , a nonexpansive map, and a closed bounded subset such that . If (1) is weakly inward and is star-shaped or (2) satisfies the Leray-Schauder boundary condition, then has a fixed point in . This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others.
On a question of Ivanov relating to nonlinear quasicontractive mappings.
On a shadowing lemma in metric spaces
In the present paper conditions are studied, under which a pseudo-orbit of a continuous map , where is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map .
On a simply connected 1-dimensional continuum without the fixed point property
On a stability theorem for the fixed-point property
On a Suzuki type general fixed point theorem with applications.
On a theorem of B. Barna.
On a theorem of Holický and Zelený concerning Borel maps without -compact fibers
The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.
On a theorem of Pachpatte
On a theorem of Popa and Noiri on multifunctions
On a theorem of van Douwen.