• Kyungpook Mathematical Journal
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• 제51권4호
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• pp.385-393
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• 2011

The aim of this paper is to introduce and study the sequence spaces [w, ${\theta}$, F, p, q]$_{\infty}({\Delta}_{\upsilon}^m)$, [w, ${\theta}$, F, p, q]$_1({\Delta}_{\upsilon}^m)$ and [w, ${\theta}$, F, p, q]$_0({\Delta}_{\upsilon}^m)$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F=(f_k)$. We establish some inclusion relations between these spaces under some conditions.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.909-931
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• 2015

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the ${\alpha}$-, ${\beta}$-, ${\gamma}$-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r,s,t,p;{\Delta})$ to X. Finally, it is proved that the sequence space $l(r,s,t,p;{\Delta})$ is rotund when $p_n$ > 1 for all n and has the Kadec-Klee property.

• 호남수학학술지
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• 제42권1호
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• pp.161-173
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• 2020

We introduce statistically localized sequences in 2-normed spaces and give some main properties of statistically localized sequences. Also, we prove that a sequence is statistically Cauchy sequence if and only if its statistical barrier is equal to zero. Moreover, we define the uniformly statistically localized sequences on 2-normed spaces and investigate its relationship with statistically Cauchy sequences.

• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.631-640
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• 2017

The aim of this paper is to introduce the binomial sequence spaces $b_0^{r,s}(\nabla)$, $b_c^{r,s}(\nabla)$ and $b_{\infty}^{r,s}(\nabla)$ by combining the binomial transformation and difference operator. We prove that these spaces are linearly isomorphic to the spaces $c_0$, c and ${\ell}_{\infty}$, respectively. Furthermore, we compute the Schauder bases and the ${\alpha}-$, ${\beta}-$ and ${\gamma}-duals$ of these sequence spaces.

• 호남수학학술지
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• 제41권4호
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• pp.725-744
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• 2019

In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (a_rtkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙²_∞.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.73-86
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• 2014

In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.657-668
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• 2022

In the present paper we introduce and study Euler sequence spaces of fractional difference and backward difference operators. We make an effort to prove that these spaces are BK-spaces and linearly isomorphic. Further, Schauder basis for Euler fractional difference sequence spaces $e^{\varsigma}_{0,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ and $e^{\varsigma}_{c,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ are also elaborate. In addition to this, we determine the 𝛼-, 𝛽- and 𝛾- duals of these spaces.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.707-722
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• 2019

For any non-negative real number ${\epsilon}_0$, we shall introduce a concept of the ${\epsilon}_0$-Cauchy sequence in a normed linear space V and also introduce a concept of the ${\epsilon}_0$-completeness in those spaces. Finally we introduce a concept of the generalized Banach spaces with these concepts.

• 대한수학회보
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• 제35권1호
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• pp.189-193
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• 1998

In this paper we construct a sequence of spaces which has Gromov-Hausdorff limit such that a geodesic in the limit space is not realized as a limit of geodesics in the spaces of the sequence. This contrasts with the result of Grove and Petersen in [1] where they proved otherwise for Alexandrov spaces with common curvature bounds.

• Journal of applied mathematics & informatics
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• 제38권3_4호
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• pp.201-209
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• 2020

We introduce and study some basic properties of rough I-convergent of triple sequence spaces and also study the set of all rough I-limits of a triple sequence spaces.