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We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.

Functional Analysis · Mathematics 2012-03-13 M. Kuchukaslan , U. Deger , O. Dovgoshey

In this paper we study some basic properties of rough $I$-convergent double sequences in the line of D$\ddot{u}$ndar [8]. We also study the set of all rough $I$-limits of a double sequence and relation between boundedness and rough…

Functional Analysis · Mathematics 2016-11-28 P. Malik , M. Maity , A. Ghosh

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…

Functional Analysis · Mathematics 2024-08-14 Nesar Hossain , Rahul Mondal

In this paper we are concerned with the recent summability notion of I-statistically pre-Cauchy real double sequences in line of Das et. al. [6] as a generalization of I-statistical convergence. Here we introduce the notion of double…

Functional Analysis · Mathematics 2017-03-22 Prasanta Malik , Argha Ghosh

In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties…

General Topology · Mathematics 2021-02-16 Amar Kumar Banerjee , Anirban Paul

The idea of rough statistical convergence for double sequences was studied by Ozcan and Or[29] in a intuitionistic fuzzy normed space. Recently the same has been generalized in the ideal context by Hossain and Banerjee[15] for sequences.…

General Mathematics · Mathematics 2023-03-27 Rahul Mondal , Nesar Hossain

In this paper, in the line of Aytar\cite{Ay2} and \c{C}olak \cite{Co}, we introduce the notion of rough statistical convergence of order $\alpha$ in normed linear spaces and study some properties of the set of all rough statistical limit…

Functional Analysis · Mathematics 2016-03-02 Manojit Maity

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…

Statistics Theory · Mathematics 2023-06-19 Joni Virta

The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…

General Topology · Mathematics 2019-07-02 AR. Murugan , J. Dianavinnarasi , C. Ganesa Moorthy

In this paper we study the notion of $\mathcal{I}$-localized and $\mathcal{I^*}$-localized sequences in $S$-metric spaces. Also, we investigate some properties related to $\mathcal{I}$-localized and $\mathcal{I}$-Cauchy sequences and give…

General Topology · Mathematics 2022-06-22 Amar Kumar Banerjee , Nesar Hossain

We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…

Functional Analysis · Mathematics 2025-06-05 Armando W. Gutiérrez , Olavi Nevanlinna

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…

Metric Geometry · Mathematics 2024-02-23 Syota Esaki , Daisuke Kazukawa , Ayato Mitsuishi

The present study introduces the notions of statistical convergence of order $\alpha$ and strong $p-$ Ces\`{a}ro summability of order $\alpha$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In…

General Mathematics · Mathematics 2023-04-06 Erdal Bayram , Çiğdem Bektaş , Yavuz Altın

In this paper we consider the notion of strong $I$-statistically pre-Cauchy double sequences in probabilistic metric spaces in line of Das et. al. [6] and introduce the new concept of strong $I^*$-statistically pre-Cauchy double sequences…

Functional Analysis · Mathematics 2019-07-09 Prasanta Malik , Argha Ghosh , Manojit Maity

In this paper we introduce and study the notion of I-convergence of sequences in a metric-like space, where I is an ideal of subsets of the set N of all natural numbers. Further introducing the notion of I*-convergence of sequences in a…

General Topology · Mathematics 2024-08-27 Prasanta Malik , Saikat Das

We study the concept of density for sets of natural numbers in some lacunary $A$-convergent sequence spaces. Also we are trying to investigate some relation between the ordinary convergence and module statistical convergence for evey…

Functional Analysis · Mathematics 2015-09-30 Ekrem Savas , Stuti Borgohain

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…

Probability · Mathematics 2008-06-13 Andreas Greven , Peter Pfaffelhuber , Anita Winter

This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…

Functional Analysis · Mathematics 2025-12-30 Abdullah Aydın , Erdal Bayram , İshak Aydın

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…

General Mathematics · Mathematics 2026-05-21 Santanu Acharjee , Sankar K. Pal

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…

Functional Analysis · Mathematics 2025-08-18 Abdullah Aydın , Mehmet Küçükaslan , Mokhwetha Mabula