• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.329-339
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• 2019

The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.525-537
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• 2005

We introduce the notions of regular preopen sets and $p^{\ast}-closed$ spaces and investigate some of these properties. Also we give a characterization of p-closed spaces.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.493-506
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• 2005

In this paper, we study the behavior and sensitivity analysis of the solution set for a system of parametric generalized nonlinear mixed quasi-variational inclusions in Banach spaces. By using some new and innovative technique, existence theorem for the system of parametric generalized nonlinear mixed quasi-variational inclusions in $L_p(p\ge2$ spaces is established. Our results improve the known result of Agarwal et al.[1].

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.57-66
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• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.401-411
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following Jensen type functional equation $$f(\frac{x-y}{n}+z)+f(\frac{y-z}{n}+x)+f(\frac{z-x}{n}+y)=f(x)+f(y)+f(z)$$ in p-Banach spaces for any fixed nonzero integer n.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.135-140
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• 2012

In this paper, we introduce the concepts of $DC^{p}_{k}$-spaces for maps which are the dual concepts of $C^{f}_{k}$-spaces for maps, and characterize $DC^{p}_{k}$-spaces for maps using the dual Gottlieb sets for maps and the LS cocategories.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1233-1242
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• 2009

In 1981 S. A. Saxon and P. P. Narayanaswami ([10]) showed that every (LF)-space has an infinite dimensional separable quotient. In this note we prove that this fails for (LF)$_{tv}$-spaces. We construct a wide class of (LF)$_{tv}$-spaces, which have no infinite dimensional separable quotient.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1377-1384
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• 2019

In this paper, we prove that for every surjective phase-isometry between the unit spheres of real atomic $L_p$-spaces for p > 0, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.73-86
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• 2014

In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.27-33
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• 1987

Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.