A Note on the Hutchinson Metric ( Draft )
نویسنده
چکیده
In Hut81], John Hutchinson introduced a metric on the set of Borel probability measures on a metric space. In this note, I present the Hutchinson metric and prove several properties of this metric. I restrict my attention to 1-bounded metric spaces. Most of the material in this note is based on Par67] and Edg98]. Proposition 7, 8 and 9 may be new.
منابع مشابه
A note on convergence in fuzzy metric spaces
The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...
متن کاملWeak $F$-contractions and some fixed point results
In this paper we define weak $F$-contractions on a metric space into itself by extending $F$-contractions introduced by D. Wardowski (2012) and provide some fixed point results in complete metric spaces and in partially ordered complete generalized metric spaces. Some relationships between weak $F$-contractions and $Fi$-contractions are highlighted. We also give some application...
متن کاملCoupled fixed point on ordered cone metric spaces with application in integral equations
Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis, 72(2010) 2259-2261.], showed that the fixed point results in the setting of cone...
متن کاملSome notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"
Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...
متن کاملHutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces
The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006