Related papers: Rough Cauchy Sequences in a Cone Metric Space
The aim of this paper is to discus the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of…
In this paper, contractive mappings of \'Ciri\'c-Matkowski type in fuzzy metric spaces are studied. A class $\Psi_1$ of gauge functions $\psi:(0,1]\to(0,1]$ such that, for any $r\in(0,1)$, there exists $\rho\in(r,1)$ such that $1-r> \tau…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…
We continue the study of ideal convergence for sequences $(x_n)$ with values in a topological space $X$ with respect to a family $\{F_\eta:\eta\in X\}$ of subsets of $X$ with $\eta\in F_\eta$, where each $F_\eta$ measures the allowed…
In this paper, we give a characterization and a some properties of a besselian sequences, which allows us to build some examples of a besselian Schauder frames. Also for a reflexive Banach spaces (with a besselian Schauder frames) we give…
The topic is the history of the concepts of equivalence relation, Cauchy sequence, and metric space. The thesis is that disused definitions of these notions could profitably be revived.
In this paper we investigate Cauchy completeness and exponentiablity for quantale enriched categories, paying particular attention to probabilistic metric spaces.
In this paper, we establish a sequential characterisation of Lebesgue fuzzy metric and explore the relationship between Lebesgue, weak G-complete and compact fuzzy metric spaces. We also discuss the Lebesgue property of several well-known…
The main aim of this paper is to study of fixed point theory in partial cone metric spaces. Infact, some common fixed point theorems for two mappings in partial cone metric spaces are obtained.
In this paper, we introduce the concept of relative convex sequences and establish their fundamental properties, highlighting their similarities to those of convex sequences. Additionally, we prove new inequalities of the Lupas and…
This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some…
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
In this paper we have introduced arithmetic ff-continuity and arithmetic fb-continuity utilizing the concept of forward and backward arithmetic convergence in quasi cone metric spaces. These concepts are used to prove some fascinating…
We consider the problem of isometric embedding of metric spaces to the Banach spaces; and introduce and study the remarkable class of so-called linearly rigid metric spaces: these are the spaces that admit a unique, up to isometry, linearly…
In this paper we present different ways to parametrize subsets of the space of valuations on $K[x]$ extending a given valuation on $K$. We discuss the methods using pseudo-Cauchy sequences and approximation types. The method presented here…
The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in…