Related papers: Rough Cauchy Sequences in a Cone Metric Space

The aim of this paper is to introduce and to investigate the basic properties of $q$-convex, $q$-affine and $q$-concave sequences and to establish their surprising connection to Chebyshev polynomials of the first and of the second kind. One…

We show that for infinite Tychonoff spaces X and Y the weak*-dual of Ck(X x Y) contains a basic sequence; moreover, the weak*-bidual of Ck(X) contains such a sequence as well. When X and Y are infinite compact spaces, we single out a…

In a metric space, such as the real numbers with their standard metric, a set A is open if and only if no sequence with terms outside of A has a limit inside A. Moreover, a metric space is compact if and only if every sequence has a…

The concept of I-statistical convergence of a double sequence was first introduced and study by Das et. el [2]. Here in this paper we discuss some results on rough ideal statistical convergence and also we introduce the notion of rough…

In these notes we discuss some relations between complex analysis (derivatives of Cauchy integrals) and curvatures of curves and surfaces. In higher dimensions the Cauchy integrals are based on generalizations of complex analysis using…

We present a formalism for analysis of linear Cauchy data on a Kottler metric. Our method removes redundancy due to gauge transformations and constraints. A set of four gauge-invariant, scalar functions on the Cauchy surface is produced and…

Soft set theory is an important and emerging area within soft computing, owing to its attribute-oriented mathematical framework and its wide applicability in diverse domains, including science and social sciences. The theoretical…

Property A introduced by Guoliang Yu is an amenability-type property for metric spaces. In this article, we study property A for uniformly locally finite coarse spaces. Main examples of coarse spaces are a metric space, a set equipped with…

We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…

In this paper, we provide equivalent characterizations of weak $G$-complete fuzzy metric spaces. Since such spaces are complete, we also characterize fuzzy metric spaces that have weak $G$-complete fuzzy metric completions. Moreover we…

A cutting sequence is a symbolic coding of a linear trajectory on a translation surface corresponding to the sequence of sides hit in a polygonal representation of the surface. We characterize cutting sequences in a regular hexagon with…

It is proved that the linearity of metric projections on subspaces and the convexity of the polars of the convex cones in the uniformly convex and uniformly smooth Banach space are equivalent, and both of them is equivalent with the fact…

We define the Ricci curvature of Markov chains on metric spaces as a local contraction coefficient of the random walk acting on the space of probability measures equipped with a Wasserstein transportation distance. For Brownian motion on a…

This paper extends the theory of rough convergence from normed linear spaces to the more abstract setting of Riesz spaces. We introduce and systematically develop the concept of rough $\mathbb{c}$-convergence ($rc$-convergence) for nets. A…

The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in…

The intrinsic unsharpness of a quantum observable is studied by introducing the notion of resolution width. This quantification of accuracy is shown to be closely connected with the possibility of making approximately repeatable…

In this paper we combine the notions of partial metric spaces with negative distances, $G_p$-metric spaces and n-metric spaces together into one structure called the partial n-metric spaces. These are generalizations of all the said…

In this paper we generalize the concept of a quasi-Cauchy sequence to a concept of a $p$-quasi-Cauchy sequence for any fixed positive integer $p$. For $p=1$ we obtain some earlier existing results as a special case. We obtain some…

Soft set theory and rough set theory are mathematical tools to deal with uncertainties. In [3], authors combined these concepts and introduced soft rough sets. In this paper, we introduce the concepts of soft rough graphs, vertex and edge…

We consider conformal metrics of constant curvature 1 on a Riemann surface, with finitely many prescribed conic singularities and prescribed angles at these singularities. Especially interesting case which was studied by C. L. Chai, C. S…