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Start Over Creator Das, Pratulananda

1. I and I∗-convergence in topological spaces

Creator:
Lahir, Benoy Kumar and Das, Pratulananda
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
I-convergence, I ∗ -convergence, condition (AP), I-limit point, and I-cluster poin
Language:
English
Description:
We extend the idea of I-convergence and I ∗ -convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Two valued measure and some new double sequence spaces in $2$-normed spaces

Creator:
Das, Pratulananda, Savas, Ekrem, and Bhunia, Santanu
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
convergence, $\mu $-statistical convergence, convergence in $\mu $-density, condition (APO$_{2}$), 2-norm, 2-normed space, paranorm, paranormed space, Orlicz function, and sequence space
Language:
English
Description:
The purpose of this paper is to introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure and an Orlicz function in $2$-normed spaces which have unique non-linear structure and to examine some of their properties. This approach has not been used in any context before.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Two valued measure and summability of double sequences

Creator:
Das, Pratulananda and Bhunia, Santanu
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
double sequences, $\mu $-statistical convergence, divergence and Cauchy criteria, convergence, divergence and Cauchy criteria in $\mu $-density, and condition (APO$_2)$
Language:
English
Description:
In this paper, following the methods of Connor \cite {connor}, we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely \cite {moe}) to $\mu $-statistical convergence and convergence in $\mu $-density using a two valued measure $\mu $. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure $\mu $ called the (APO$_2$) condition, inspired by the (APO) condition of Connor \cite {jc}. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure $\mu $ has the condition (APO$_2$).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public