• Honam Mathematical Journal
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• v.26 no.2
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• pp.137-145
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• 2004

we shall study some properties of a new class ($\sqrt[\kappa]{P}$) (defined below). Also we show that T may not be normaloid when $T{\in}(\sqrt[\kappa]{P})$, and that the class ($\sqrt{H}$) may not have the translation-invariant propety.

• Journal of the Korean Institute of Navigation
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• v.20 no.1
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• pp.87-96
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• 1996

In this paper, The Fuzzy Logic Controller based on T-operators is designed. Some typical T-operators and their mathematical properties are studied. A generalized fuzzy inference model is proposed by introducing the general notion of T-operators into the conventional one which is based only on the Min and Max operators. Fuzzy Logic Control algorithms based on the T-operators are suggested. Then, by computer simulations, the effect of various T-operators on the performance of the fuzzy logic controller are studied. The purpose of these simulation studies were to observe the flexibility and system responses using the processed class of T-operators in the fuzzy inference mechanisms. This observation was made on parameters such as speed of reponses, steady-state behavior and non oscillatory responses.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.99-116
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• 2017

The aim of this article is to introduce a new form of Kantorovich $Sz{\acute{a}}sz$-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.225-251
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• 2018

The m-isometry of a single operator in Agler and Stankus [3] was naturally generalized to the m-isometric tuple of several commuting operators by Gleason and Richter [22]. Some examples of m-isometric tuples including the recently much studied Arveson-Drury d-shift were given in [22]. We provide more examples of m-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of m-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter [22] are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the m-isometry of a single operator.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.255-272
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• 2005

This paper is concerned with studying the weighted $L^P$ boundedness of a class of maximal operators related to homogeneous singular integrals with rough kernels. We obtain appropriate weighted $L^P$ bounds for such maximal operators. Our results are extensions and improvements of the main theorems in [2] and [5].

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.35-39
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• 2013

Let $(class{\mathcal{A}})^*$ denotes the class of operators satisfying ${\mid}T^2{\mid}{\geq}{\mid}T^*{\mid}^2$. In this paper, we show that the spectrum is continuous on $(class{\mathcal{A}})^*$.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.205-209
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• 2011

Let $\mathcal{QA}$ denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality $T^*|T^2|T{\geq}T^*|T|^2T$. Let $f$ be an analytic function defined on an open neighbourhood $\mathcal{U}$ of ${\sigma}(T)$ such that $f$ is non-constant on the connected components of $\mathcal{U}$. We generalize a theorem of Sheth [10] to $f(T){\in}\mathcal{QA}$.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.311-317
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• 2013

In this note we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ with symbol in the class of functions $f+\bar{g}$ with polynomials $f$ and $g$ of degree 2.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.235-246
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• 2010

A Banach space operator A $\in$ B(X) is polaroid if the isolated points of the spectrum of A are poles of the resolvent of A; A is hereditarily polaroid, A $\in$ ($\mathcal{H}\mathcal{P}$), if every part of A is polaroid. Let $X^n\;=\;\oplus^n_{t=i}X_i$, where $X_i$ are Banach spaces, and let A denote the class of upper triangular operators A = $(A_{ij})_{1{\leq}i,j{\leq}n$, $A_{ij}\;{\in}\;B(X_j,X_i)$ and $A_{ij}$ = 0 for i > j. We prove that operators A $\in$ A such that $A_{ii}$ for all $1{\leq}i{\leq}n$, and $A^*$ have the single-valued extension property have spectral properties remarkably close to those of Jordan operators of order n and n-normal operators. Operators A $\in$ A such that $A_{ii}$ $\in$ ($\mathcal{H}\mathcal{P}$) for all $1{\leq}i{\leq}n$ are polaroid and have SVEP; hence they satisfy Weyl's theorem. Furthermore, A+R satisfies Browder's theorem for all upper triangular operators R, such that $\oplus^n_{i=1}R_{ii}$ is a Riesz operator, which commutes with A.

• Journal of the Korean Society for information Management
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• v.10 no.1
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• pp.53-63
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• 1993

The conventional fuzzy set model has been criticized as a retrieval model because the MIN and MAX operators have the properties adverse to effective calculation of document values. Since the first introduction of fuzzy set theory a variety of fuzzy operators have been developed, which can replace the MIN and MAX operators. We analyze their behavioral aspects of generating document values, and propose the enhanced fuzzy set model based on a class of fuzzy operators called positively compensatory operators. We also show through performance experiments that the proposed fuzzy set model provides higher retrieval effectiveness.