• Honam Mathematical Journal
• /
• v.7 no.1
• /
• pp.129-133
• /
• 1985

The object of this note is to discuss the relationship between some matrix transformations that naturally occur involving prime numbers in the theory of Summability.

• Korean Journal of Mathematics
• /
• v.27 no.4
• /
• pp.949-968
• /
• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.1093-1103
• /
• 2011

We give the characterizations of the classes of matrix trans-formations ($m(\phi),{\ell}_p$), ($n(\phi),{\ell}_p$) ([5, Theorem 2]), (${\ell}_p,m(\phi)$) ([5, Theorem 1]) and (${\ell}_p,n(\phi)$) for $1{\leq}p{\leq}{\infty}$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.

• Journal of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.127-136
• /
• 2013

The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks $k$ and $l$.

• Communications of the Korean Mathematical Society
• /
• v.20 no.4
• /
• pp.723-729
• /
• 2005

Let F be a non-trivial non-Archimedian field. The sequence spaces $\Gamma\;(F)\;and\;{\Gamma}^{\ast}(F)$ were defined and studied by Soma-sundaram[4], where these spaces denote the spaces of entire and analytic sequences defined over F, respectively. In 1997, these spaces were generalized by Mursaleen and Qamaruddin[1] by considering an arbitrary sequence $U\;=\;(U_k),\;U_k\;{\neq}\;0 \;(\;k\;=\;1,2,3,{\cdots})$. They characterized some classes of infinite matrices considering these new classes of sequences. In this paper, we further generalize the above mentioned spaces and define the spaces $\Gamma(u,\;F,\;{\Delta}),\;{\Gamma}^{\ast}(u,\;F,\;{\Delta}),\;l_p(u,\;F,\;{\Delta})$), and $b_v(u,\;F,\;{\Delta}$). We also study some matrix transformations on these new spaces.

• Communications of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.277-294
• /
• 2016

The aim of this paper is to present the classical sets of sequences and related matrix transformations with respect to the b-metric. Also, we introduce the relationships between these sets and their classical forms with corresponding properties including convergence and completeness. Further we determine the duals of the new spaces and characterize matrix transformations on them into the sets of b-bounded, b-convergent and b-null sequences.

• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.271-289
• /
• 2018

Let 0 < q < ${\infty}$. In this study, we introduce the spaces ${\mathcal{BV}}_q$ and ${\mathcal{LS}}_q$ of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix ${\Delta}$ and summation matrix S in the space ${\mathcal{L}}_q$ of absolutely q-summable double sequences, respectively. Also, we determine their ${\alpha}$- and ${\beta}-duals$ and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q ${\leq}$ 1.

• Honam Mathematical Journal
• /
• v.44 no.1
• /
• pp.26-35
• /
• 2022

In this paper we introduce two type of representations of the Pascal matrix via induced transformations of some q-derivatives as well as their some combinatorial applications.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.9 no.9
• /
• pp.3611-3634
• /
• 2015

In this paper, we build a theoretical framework for quantitatively measuring and graphically representing the degrees of closeness centralization among performers assigned to enact a workflow procedure. The degree of closeness centralization of a workflow-performer reflects how near the performer is to the other performers in enacting a corresponding workflow model designed for workflow-supported organizational operations. The proposed framework comprises three procedural phases and four functional transformations, such as discovery, analysis, and quantitation phases, which carry out ICN-to-WsoN, WsoN-to-SocioMatrix, SocioMatrix-to-DistanceMatrix, and DistanceMatrix-to-CCV transformations. We develop a series of algorithmic formalisms for the procedural phases and their transformative functionalities, and verify the proposed framework through an operational example. Finally, we expatiate on the functional expansion of the closeness centralization formulas so as for the theoretical framework to handle a group of workflow procedures (or a workflow package) with organization-wide workflow-performers.

• Korean Journal of Mathematics
• /
• v.28 no.2
• /
• pp.205-221
• /
• 2020

Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space |𝜙_z|(p) over the paranormed space ℓ(p) using Euler totient means, where p = (p_k) is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the α-, β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|𝜙_z|(p), λ) and (λ, |𝜙_z|(p)), where λ is any given sequence space.