• Honam Mathematical Journal
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• v.42 no.2
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• pp.251-268
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• 2020

In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree's K-functional for the bivariate Szász-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szász-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bögel continuous functions.

• 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.6 no.2
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• pp.323-329
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• 1998

In this paper, we introduce a new class of sets, called $m$-sets, and the notion of $m$-continuity. In particular, $m$-sets and $m$-continuity are used to extend known results for ${\alpha}$-continuity and semi-continuity and precontinuity.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.1089-1104
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• 2014

An operator $T{\in}L(H)$, is said to belong to k-quasi class $A_n^*$ operator if $$T^{*k}({\mid}T^{n+1}{\mid}^{\frac{2}{n+1}}-{\mid}T^*{\mid}^2)T^k{\geq}O$$ for some positive integer n and some positive integer k. First, we will see some properties of this class of operators and prove Weyl's theorem for algebraically k-quasi class $A_n^*$. Second, we consider the tensor product for k-quasi class $A_n^*$, giving a necessary and sufficient condition for $T{\otimes}S$ to be a k-quasi class $A_n^*$, when T and S are both non-zero operators. Then, the existence of a nontrivial hyperinvariant subspace of k-quasi class $A_n^*$ operator will be shown, and it will also be shown that if X is a Hilbert-Schmidt operator, A and $(B^*)^{-1}$ are k-quasi class $A_n^*$ operators such that AX = XB, then $A^*X=XB^*$. Finally, we will prove the spectrum continuity of this class of operators.

• Journal of the Korean Society of Clothing and Textiles
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• v.27 no.6
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• pp.675-684
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• 2003

The purposes of this study was to identify the dimensions of salesperson's effort and to examine the effect of salesperson's effort on relationship quality and customer intent to relationship continuity of middle upper class older female customers. The subjects used for the study were 202 middle upper class older female customers over 55 years living in Seoul. Factor analysis, paired t-test, multiple regression analysis and path analysis were used for statistics analysis. The results of this study were as follows. First, 5 factors were identified for the dimensions of salesperson's effort in older female customer's perception: attentiveness/product competence/effective access/friendliness/ special treatment. The salesperson's effort perceived most importantly was friendliness. Second, the salesperson's effort perceived by customer had direct and indirect effects on customer intent to relationship continuity; indirect effect mediated by relationship quality was larger than the direct one. Relationship quality was proved to have a crucial role in customer intent to relationship continuity. The influences of dimensions of salesperson's effort were also investigated. The effective access affected considerably on customer intent to relationship continuity.

• East Asian mathematical journal
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• v.19 no.2
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• pp.291-303
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• 2003

A result of Hardy and Littlewood relates Holder continuity of analytic functions in the unit disk with a bound on the derivative. Gehring and Martio extended this result to the class of uniform domains. In this paper we obtain a similar result to the class of uniformly John domains in terms of the inner diameter metric. We give several properties of a domain with the property. Also we show some results on the Holder continuity of conjugate harmonic functions in the above domains.

• East Asian mathematical journal
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• v.18 no.2
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• pp.183-193
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• 2002

The aim of this paper is to prove a common fixed point theorem from the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in fuzzy metric spaces.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.119-130
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• 2006

A new class of functions is introduced in this paper. This class is called almost ${\delta}$-precontinuity. This type of functions is seen to be strictly weaker than almost precontinuity. By using ${\delta}$-preopen sets, many characterizations and properties of the said type of functions are investigated.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.303-315
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• 2014

In this work, we construct Kantorovich type generalization of a class of linear positive operators via Riemann type q-integral. We obtain estimations for the rate of convergence by means of modulus of continuity and the elements of Lipschitz class and also investigate weighted approximation properties.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.355-379
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• 2024

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.