Many authors have been using the Hausdorffmetric to obtain fixed point and coincidence point theorems for multimaps on a metric space. In most cases, the metric nature of the Hausdorff metric is not used and the existence part of theorems can be proved without using the concept of Hausdorff metric under much less stringent conditions on maps. The aim of this paper is to illustrate this and to o...

We explore in depth the theory behind deterministic fractals by investigat­ ing transformations on metric spaces and the contraction mapping theorem. In doing so we introduce the notion of the Hausdorff distance metric and its connection to the space of fractals. In order to understand how deterministic fractals are generated, we develop the concept of an iterated function system (IFS) and what...

In [1] the pseudo-metric dist min on compact subsets A and B of a topological space generated from arbitrary metric space is defined. Using this notion we define the Hausdorff distance (see e.g. [5]) of A and B as a maximum of the two pseudo-distances: from A to B and from B to A. We justify its distance properties. At the end we define some special notions which enable to apply the Hausdorff d...

We show that Bowen’s equation, which characterises the Hausdorff dimension of certain sets in terms of the topological pressure of an expanding conformal map, applies in greater generality than has been heretofore established. In particular, we consider an arbitrary subset Z of a compact metric space and require only that the lower Lyapunov exponents be positive on Z, together with a tempered c...

In [2] the pseudo-metric distmax min on compact subsets A and B of a topological space generated from arbitrary metric space is defined. Using this notion we define the Hausdorff distance (see e.g. [6]) of A and B as a maximum of the two pseudo-distances: from A to B and from B to A. We justify its distance properties. At the end we define some special notions which enable to apply the Hausdorf...

Fuzzy Mathematics has seen an enormous growth since the introduction of notion of fuzzy sets by Zadeh in 1965. Kramosil and Michalek introduced the notion of fuzzy metric spaces which was later modified by George and Veeramani and others. The notion of intuitionistic fuzzy metric spaces was introduced by Park in 2004. Many authors have studied fixed point and common fixed theorems for mappings ...

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

There are two fundamental results in the classical theory of metric Diophantine approximation: Khintchine’s theorem and Jarńık’s theorem. The former relates the size of the set of well approximable numbers, expressed in terms of Lebesgue measure, to the behavior of a certain volume sum. The latter is a Hausdorff measure version of the former. We start by discussing these theorems and show that ...

Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced...