• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.723-730
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• 2004

The definition of a D-admissible fuzzy subset for an operator domain D on a group G is modified to obtain new kinds of (${\in},\;{\in}\;{\vee}q$)-fuzzy subgroups such as an (${\in},\;{\in}\;{\vee}q$)-fuzzy normal subgroup, an (<${\in},\;{\in}\;{\vee}q$)-fuzzy characteristic subgroup, an (<${\in},\;{\in}\;{\vee}q$)-fuzzy fully invariant subgroup which are invariant under D. As results, some of the fundamental properties of such (${\in},\;{\in}\;{\vee}q$)-fuzzy subgroups are obtained.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.37-44
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• 2000

In this paper, for a given p-adic quasicharacter $c_{v}$ : $k_{v}$longrightarrow $Q_{p}$ satisfying a special condition, we will explicitly construct an admissible pairing corresponding to $c_{v}$. We define a p-adic height on the arbitrary abelian varieties associated to divisors and $c_{v}$ by using admissible pairings at every nonarchimedean places. We also show that our p-adic height satisfies similar properties of Neron-Tate's canonical p-adic height.t.ght.t.t.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.63-78
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• 2008

We generalize several integral inequalities for analytic functions on the open unit polydisc $U^n={\{}z{\in}C^n||zj|<1,\;j=1,...,n{\}}$. It is shown that if a holomorphic function on $U^n$ belongs to the mixed norm space $A_{\vec{\omega}}^{p,q}(U^n)$, where ${\omega}_j(\cdot)$,j=1,...,n, are admissible weights, then all weighted derivations of order $|k|$ (with positive orders of derivations) belong to a related mixed norm space. The converse of the result is proved when, p, q ${\in}\;[1,\;{\infty})$ and when the order is equal to one. The equivalence of these conditions is given for all p, q ${\in}\;(0,\;{\infty})$ if ${\omega}_j(z_j)=(1-|z_j|^2)^{{\alpha}j},\;{\alpha}_j>-1$, j=1,...,n (the classical weights.) The main results here improve our results in Z. Anal. Anwendungen 23 (3) (2004), no. 3, 577-587 and Z. Anal. Anwendungen 23 (2004), no. 4, 775-782.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.69-83
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• 2009

New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Frechet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.829-832
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• 1999

This to correct Section 4 of our previous work [1].

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.509-520
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• 2003

Let p be a prime number, $Q_{p}$ the field of p-adic numbers, K a finite extension of $Q_{p}$, $\bar{K}}$ a fixed algebraic closure of K and $C_{p}$ the completion of K with respect to the p-adic valuation. Let E be a closed subfield of $C_{p}$, containing K. Given elements $t_1$...,$t_{r}$ $\in$ E for which the field K($t_1$...,$t_{r}$) is dense in E, we construct integral bases of E over K.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.85-101
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• 1999

Let $p$ be analytic in the unit disc U and let $q$ be univalent in U. In addition, let ${\Omega}$ be a set in C and let ${\psi}:c^3{\times}U{\rightarrow}C$. The author determines conditions on ${\psi}$ so that $$\{{\psi}(p(z),zp^{\prime}(z),z^2p^{{\prime}{\prime}}(z);z){\mid}z{\in}U\}{\subset}{\Omega}{\Rightarrow}p(U){\subset}q(U)$$. Applications of this result to differential inequalities, differential subordinations and integral inequalities are presented.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.503-519
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• 2015

In this work, certain classes of admissible functions are considered. Some strong dierential subordination and superordination properties of analytic functions associated with new generalized derivative operator $B^{{\mu},q,s}_{{\lambda}_1,{\lambda}_2,{\ell},d}$ are investigated. New strong dierential sandwich-type results associated with the generalized derivative operator are also given.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1017-1029
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• 2010

In this paper we obtain a very general theorem of $\rho$-compatibility for three multivalued mappings, one of them from the class $\mathfrak{B}$. More exactly, we show that given a G-convex space Y, two topological spaces X and Z, a (binary) relation $\rho$ on $2^Z$ and three mappings P : X $\multimap$ Z, Q : Y $\multimap$ Z and $T\;{\in}\;\mathfrak{B}$(Y,X) satisfying a set of conditions we can find ($\widetilde{x},\;\widetilde{y}$) ${\in}$ $X\;{\times}\;Y$ such that $\widetilde{x}\;{\in}\;T(\widetilde{y})$ and $P(\widetilde{x}){\rho}\;Q(\widetilde{y})$. Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.