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2007, Int. J. Contemp. Math. Sciences
In this article we introduce I-lacunary convergence of sequences in 2-normed spaces.
2018
In this paper, we study concepts of I -convergence, I ∗-convergence, I -Cauchy and I ∗-Cauchy sequences of functions and investigate relationships between them and some properties in 2-normed spaces.
2018
In this paper, we study concepts of $\mathcal{I}$-convergence, $\mathcal{I}^*$-convergence, $\mathcal{I}$-Cauchy and $\mathcal{I}^*$-Cauchy sequences of functions and investigate relationships between them and some properties in $2$-normed spaces.
Universal Journal of Mathematics and Applications
In this study, we introduced the concepts of I 2-convergence and I * 2-convergence of double sequences of functions in 2-normed space. Also, were studied some properties about these concepts and investigated relationships between them for double sequences of functions in 2-normed spaces.
The object of this paper is to introduce some new sequence spaces related with the concept of lacunary strong almost convergence for double sequences and also to characterize these spaces through sublinear functionals that both dominate and generate Banach limits and to establish some inclusion relations.
2019
Throughout the paper, N denotes the set of all positive integers and R the set of all real numbers. The concept of convergence of a sequence of real numbers has been extended to statistical convergence independently by Fast [14] and Schoenberg [32]. Gökhan et al. [19] introduced the notion of pointwise and uniform statistical convergence of double sequences of real-valued functions. The idea of I -convergence was introduced by Kostyrko et al. [25] as a generalization of statistical convergence which is based on the structure of the ideal I of subset of N [14, 15]. Gezer and Karakuş [18] investigated I -pointwise and uniform convergence and I ∗-pointwise and uniform convergence of function sequences and they examined the relation between them. Baláz et al. [4] investigated I -convergence and I -continuity of real functions. Das et al. [6] introduced the concept of I -convergence of double sequences in a metric space and studied some properties of this convergence. Dündar and Altay [7...
A function $f$ defined on a 2-normed space $ (X,||.,.||)$ is ward continuous if it preserves quasi-Cauchy sequences where a sequence $(x_n)$ of points in $X$ is called quasi-Cauchy if $lim_{n\rightarrow\infty}||\Delta x_{n},z||=0$ for every $z\in X$. Some other kinds of continuties are also introduced via quasi-Cauchy sequences in 2-normed spaces. It turns out that uniform limit of ward continuous functions is again ward continuous.
Annals of the University of Craiova, Mathematics and Computer Science Series
In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.
Applied Mathematics Letters, 2007
In 1989, Das and Patel considered known sequence spaces to define two new sequence spaces called lacunary almost convergent and lacunary strongly almost convergent sequence spaces, and proved two inclusion theorems with respect to those spaces. In this paper, we shall extend those spaces to two new double sequence spaces and prove multidimensional analogues of Das and Patel's results.
Abstract and Applied Analysis, 2013
We study some new strongly almost lacunary -convergent generalized difference sequence spaces defined by an Orlicz function. We give also some inclusion relations related to these sequence spaces.
2011
The main object of this paper is to introduce a new sequence space by using lacunary sequence and investigate both the modular structure with some geometric properties and some topological properties with respect to the Luxemburg norm.
In this paper we introduce I-lacunary convergence of generalized difference sequences by using a sequence of moduli in n-normed space.
2015
In this paper we introduce I-lacunary convergence of generalized difference sequences by using a sequence of moduli in n-normed space.
2020
c © by University of Niš, Serbia | Creative Commons Licence: CC BY-NC-ND Abstract. In this study, firstly, we studied some properties of I2-convergence. Then, we introduced I2-Cauchy and I∗ 2 -Cauchy sequence of double sequences of functions in 2-normed space. Also, we investigated the relationships between them for double sequences of functions in 2-normed spaces.
Kyungpook mathematical journal, 2012
In this article we introduce the concepts of lacunary I-convergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.
Facta Universitatis, Series: Mathematics and Informatics
In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.
Acta Mathematica Vietnamica, 2013
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Abstract and Applied Analysis, 2014
We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong (A)-convergence, whereA=(aik)is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.
Taiwanese Journal of Mathematics, 2007
In this paper we introduce and investigate I−convergence in 2− normed spaces, and also define and examine some new sequence spaces using 2−norm.
In this paper we define three classes of new double sequence spaces. We give some relations related to these sequence spaces. We also introduce the concept of double lacunary statistical Zweier convergence and obtain some inclusion relations related to these new double sequence spaces.
Communications in Advanced Mathematical Sciences
In this work, we discuss various types of $\mathcal{I}_2$-uniform convergence and equi-continuous for double sequences of functions. Also, we introduce the concepts of $\mathcal{I}_2$-uniform convergence, $\mathcal{I}_2^*$-uniform convergence, $\mathcal{I}_2$-uniformly Cauchy sequences and $\mathcal{I}_2^*$-uniformly Cauchy sequences for double sequences of functions in $2$-normed spaces. Then, we show the relationships between these new concepts.
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