Related papers: Cone Normed Spaces and Weighted Means
A unified version of Machado-Bishop theorem in weighted spaces is given. A number of applications illustrate its importance.
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some…
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
In this paper we investigate the metric properties of quadrics and cones of the $n$-dimensional Euclidean space. As applications of our formulas we give a more detailed description of the construction of Chasles and the wire model of…
This article aims to extend classical homological results about the rational normal curves to analogues in weighted projective spaces. Results include determinantality and nonstandard versions of quadratic generation and the Koszul…
Here we present an overview of countably-normed spaces. We discuss the main topologies--weak, strong, and inductive--placed on the dual of a countably-normed space and discuss the sigma-fields generated by these topologies. In particular,…
This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We provide a simple characterisation of multigeodesic normed…
For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman…
In this paper, we study the fixed point theory for multi-valued mappings on partial cone metric spaces. We prove an analogous to the well-known Kannan$'s$ fixed point theorem and Chatterjea$'s$ fixed point theorem for multi-valued mappings…
In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose,…
Some boundedness properties of function spaces (considered as topological groups) are studied.
We classify rotational surfaces in a normed 3-space with rotationally symmetric norm whose principal curvatures satisfy a linear relation.
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
In this paper we investigate the properties of function spaces using the selection principles.
We are going to classify sets by a given mean in two ways. Firstly we study small and big sets regarding a given mean. Secondly we study sets that have the same weight according to a mean. We also generalize the notion of roundness and get…
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…
In this article, we prove some fixed point theorems in metric type spaces. This article is just a generalization some results previously proved in \cite{niyi-gaba}. In particular, we give some coupled common fixed points theorems under weak…