Equivalent definitions of BV space and of total variation on metric measure spaces
نویسندگان
چکیده
منابع مشابه
Quasi-contractive Mappings in Fuzzy Metric Spaces
We consider the concept of fuzzy quasi-contractions initiated by '{C}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{H}$-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani.The results are illustrated by a representative example.
متن کاملOn the Structure of Metric-like Spaces
The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...
متن کاملSobolev and BV spaces on metric measure spaces via derivations and integration by parts
We develop a theory of BV and Sobolev Spaces via integration by parts formula in abstract metric spaces; the role of vector fields is played by Weaver’s metric derivations. The definition hereby given is shown to be equivalent to many others present in literature. Introduction In the last few years a great attention has been devoted to the theory of Sobolev spaces W 1,q on metric measure spaces...
متن کاملCommon Fixed Point Results on Complex-Valued $S$-Metric Spaces
Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...
متن کاملCompleteness in Probabilistic Metric Spaces
The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...
متن کامل