• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.499-507
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• 2010

In this note, we study the local spectral properties of semi-shifts. If $T\;{\in}\;L(X)$ is a semi-shift on a complex Banach space X, then T is admissible. We also prove that if $T\;{\in}\;L(X)$ is subadmissible, then $X_T(F)\;=\;E_T(F)$ for all closed $F\;{\subseteq}\;\mathbb{C}$. In particular, every subscalar operator on a Banach space is admissible.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.349-357
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• 1996

Using a special property of Bloch functions with Hardmard gaps and using the geometric properties of the self maps of the unit disc, we give a way of constructing explicit examples of Bloch functions f whose derivative is in $H^p$ (0 < p < 1) but $f \notin BMOA$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1643-1653
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• 2019

This paper shows that if $1<p<{\infty}$, ${\alpha}{\geq}-n-2$, ${\alpha}>-1-{\frac{p}{2}}$ and f is holomorphic on the unit ball ${\mathbb{B}}_n$, then $${\int_{{\mathbb{B}}_n}}{\mid}Rf(z){\mid}^p(1-{\mid}z{\mid}^2)^{p+{\alpha}}dv_{\alpha}(z)<{\infty}$$ if and only if $${\int_{{\mathbb{B}}_n}}{\int_{{\mathbb{B}}_n}}{\frac{{\mid}f(z)-F({\omega}){\mid}^p}{{\mid}1-(z,{\omega}){\mid}^{n+1+s+t-{\alpha}}}}(1-{\mid}{\omega}{\mid}^2)^s(1-{\mid}z{\mid}^2)^tdv(z)dv({\omega})<{\infty}$$ where s, t > -1 with $min(s,t)>{\alpha}$.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.343-359
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• 2021

The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $f({\sqrt[k]{x^k+z^k}},\;{\sqrt[{\ell}]{y^{\ell}+w^{\ell}}})=f(x,y)+f(z,w)$, x, y, z, w ∈ ℝ, for f a mapping from the set of all real numbers ℝ into a vector space, where k and ℓ are fixed positive integers. Also using the fixed point result of Brzdęk and Ciepliński [11, Theorem 1] in (2, 𝛽)-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2061-2070
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• 2013

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.907-913
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• 2013

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(2x_1)+f(2x_2)+{\cdots}+f(2x_n){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that 2${\leq}$t

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.179-190
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• 2007

In this paper, we consider the general variational inequality GVI(F, g, C), where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type method $u_{n+l}=(1-{\alpha}+{\theta}_{n+1})Tu_n+{\alpha}u_n-{\theta}_{n+1g}(Tu_n)-{\lambda}_{n+1}{\mu}F(Tu_n),\;n{\geq}0$. for solving the general variational inequalities. The sequence $\{x_n}\$ is shown to converge in norm to the solutions of the general variational inequality GVI(F, g, C) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Results proved in the paper can be viewed as an refinement and improvement of previously known results.

• Journal of architectural history
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• v.7 no.4 s.17
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• pp.29-47
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• 1998

The aim of this study is to understand the original methods of architectural composition in F. L. Wright's works, For this purpose, the principal thoughts based on his organic architecture was examined over all others, and the results of this study are as follows. 1. F. L. Wright knew Taoist Philosophy, especially Lao-tzu's thought about space based on traditional oriental arts included traditional japanese arts by his superior intuition. this is similar to Froebel Thought in the principal theory, that is, his own unique field of abstract architectural education with three-dimensional geometry learned through Froebel Gifts. 2. Space is reality ; such Lao-tzu's thought, reversed the sense of values, influenced F. L. Wright's way to accomplish his own continuous space. that is to say, he attempted taking precedence of spatial organization by the unit of three-dimensional module made the substance, Froebel Blocks (3, 4, 5, 6 Gifts) into non-substance, and trying to do the methods of continuous liberal composition in architecture. which is his original accomplishment, namely his mentioned 'democratic' because of judging the space and the mold of architecture as individualities. 3. F. L. Wright treated the space as a positive entity, so that he created his own architecture organically combined with spaces and forms. : This was the result that he comprehended both formative, physical worth in West and spatial, non-physical worth in East as equivalence. It is understood that F. L. Wright's works combined with East and West are the significance of his architecture and the progress of true internationalities and modernization in modern architecture. 4. From the analyses of his works, we knew the fact that F. L. Wright's architecture, especially in the spatial organization were performed by the reasonable methods with geometric system of Froebel Gifts. In the observation of our fundamental way of thinking on his architecture, this study shows the necessity to let us get out of preconceptions and conclusions that the organic architecture is mysterious and difficult, but to systematize and put his organic methods to practical use.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.287-293
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• 2010

It is well known that there is a residual subset J of the space of $C^1$-diffeomorphisms on a compact Riemannian manifold M such that the maps f $\mapsto$ chain recurrent set of f and f $\mapsto$ number of chain components of f are continuous on J. In this paper we get the flow version of the above results on diffeomorphisms.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.237-252
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• 2014

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.