相关论文: A criterion for Cauchy sequences in db-metric spac…

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…

Some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces and some applications are given.

We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with…

We study cross ratios from an axiomatic viewpoint, also known as the study of M\"obius spaces. We characterise cross ratios induced by quasi-metrics in terms of topological properties of their image. Furthermore, we generalise the notions…

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 note we introduce and define half Cauchy sequences. We prove that a sequence of real numbers is convergent if and only if it is bounded and half Cauchy. We also provide an example of how the concept may be used.

A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found.

We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.

It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present…

We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.

In this research article, we have primarily focused on the circumstantial investigation of deferred statistical convergence of sequences and investigated some fundamental results compatible with the structure of a probabilistic normed…

In this paper, we introduce the concept of partial extended b-metric spaces (PEBMS) as a unification and generalization of extended b-metric spaces and partial b-metric spaces. This new structure incorporates a point-dependent control…

We prove a general inequality for more than two sequences mirroring that of the discrete two-sequence Cauchy-Schwarz.

An internal characterization of complete metric mappings (by means of Cauchy nets tied at a point) is given and a construction of the completion of a metric mapping is presented.

Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori…

This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…

In this paper, we prove a `cut-by-curves criterion' for the overconvergence of integrable connections on certain rigid analytic spaces and certain varieties over $p$-adic fields.

In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are…

We describe an explicit metric that induces the Chabauty topology on the space of closed subsets of a proper metric space M.

In this paper we investigate Cauchy completeness and exponentiablity for quantale enriched categories, paying particular attention to probabilistic metric spaces.