• 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.

• 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.

• 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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• 제28권2호
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• pp.361-378
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• 2020

The most apparent aspect of the present study is to introduce a new sequence space 𝚽^⋆(𝓛_p) derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the α-, β(bp)- and γ-duals of the space 𝚽^⋆(𝓛_p) are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.25-40
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• 2021

In this article we introduce tribonacci sequence spaces c0(T) and c(T) derived by the domain of a newly defined regular tribonacci matrix T. We give some topological properties, inclusion relations, obtain the Schauder basis and determine ��-, ��- and ��- duals of the spaces c0(T) and c(T). We characterize certain matrix classes (c0(T), Y) and (c(T), Y), where Y is any of the spaces c0, c or ℓ∞. Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space c0(T).