• Korean Journal of Mathematics
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• v.17 no.1
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• pp.37-41
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• 2009

We would like to propose Dirichlet-Jordan theorem on the space of summable in measure(SIM). Surely, this is a kind of extension of bounded variation([1, 4]), and considered as an application of fuzzy set such that ${\alpha}$-cut is 0.

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

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.535-540
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• 2006

In this paper, characterizations of difference quotient transformation in the Krein space which is contained continuously and contractively in the krein space of square summable power series C (z) is obtained from the complementation theory.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.447-459
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• 1995

A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].

• The Mathematical Education
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• v.21 no.3
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• pp.7-11
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• 1983

A measurable function f defined on a measurable subset A of the real line R is called pth power summable on A if │f│$^{p}$ is integrable on A and the set of all pth power summable functions on A is denoted by L$^{p}$ (A). For each member f in L$^{p}$ (A), we define ∥f∥$_{p}$ =(equation omitted) For real numbers p and q where (equation omitted) and (equation omitted), we discuss the Holder's inequality ∥fg∥$_1$<∥f∥$_{p}$ ∥g∥$_{q}$ , f$\in$L$^{p}$ (A), g$\in$L$^{q}$ (A) and the Minkowski inequality ∥＋g∥$_{p}$ <∥f∥$_{p}$ ＋∥g∥$_{p}$ , f,g$\in$L$^{p}$ (A). In this paper also discuss that L$_{p}$ (A) becomes a metric space with the metric $\rho$ : L$^{p}$ (A) $\times$L$^{p}$ (A) longrightarrow R where $\rho$(f,g)=∥f-g∥$_{p}$ , f,g$\in$L$^{p}$ (A). Then, in this paper prove the Riesz-Fischer theorem, i.e., the space L$^{p}$ (A) is complete and that the space L$^{p}$ (A) is separable.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.659-668
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• 2001

Let S(z) be a power series with operator coefficients such that multiplication by S(z) is an everywhere defined transformation in the square summable power series C(z). In this paper we show that there exists a reproducing kernel Krein space which is state space of extended canonical linear system with transfer function S(z). Also we characterize the reproducing kernel function of the state space of a linear system.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.91-103
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• 2018

In this paper, we generalize the concept of deferred density to that of deferred f-density, where f is an unbounded modulus and introduce a new non-matrix convergence method, namely deferred f-statistical convergence or $S^f_{p,q}$-convergence. Apart from studying the $K{\ddot{o}}the$-Toeplitz duals of $S^f_{p,q}$, the space of deferred f-statistically convergent sequences, a decomposition theorem is also established. We also introduce a notion of strongly deferred $Ces{\grave{a}}ro$ summable sequences defined by modulus f and investigate the relationship between deferred f-statistical convergence and strongly deferred $Ces{\grave{a}}ro$ summable sequences defined by f.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1051-1067
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• 2023

In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.755-772
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• 2004

We show that the Fourier-Laplace series of a distribution on the sphere is uniformly Cesaro-summable to zero on a neighborhood of a point if and only if this point does not belong to the support of the distribution. Similar results on the ball and on the real projective space are also proved.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.137-147
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• 2012

In this paper we introduce some new double sequence spaces via ideal convergence and an Orlicz function in $n$-normed spaces and examine some properties of the resulting spaces.