• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.105-112
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• 2022

Let g : X ⟶ Y and f : Y ⟶ Z be two maps between real normed linear spaces. Then f is called generalized isometry or g-isometry if for each x, y ∈ X, ║f(g(x)) - f(g(y))║ = ║g(x) - g(y)║. In this paper, under special hypotheses, we prove that each generalized isometry is affine. Some examples of generalized isometry are given as well.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.195-202
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• 2007

We prove that a real hypersurface M in a complex space form Mn(c), $c{\neq}0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution and the Ricci operator is ${\eta}-parallel$, is a Hopf hypersurface. We also give a characterization of this hypersurface.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.235-244
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• 2006

We shall give a characterization of a real hypersurface M in a complex space form Mn(c), $c\;{\neq}\;0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution of M, and the Ricci operator is ${\eta}-parallel$.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.345-352
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• 2011

In this article we introduce the fuzzy real valued double sequence spaces $_2{\ell}^F$ (p) where p = ($p_{nk}$) is a double sequence of bounded strictly positive numbers. We study their different properties like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results also.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.189-200
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• 2012

In this article we introduce the class of I-convergent double sequences of fuzzy real numbers. We have studied different properties like solidness, symmetricity, monotone, sequence algebra etc. We prove that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.55-60
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• 2021

Let M be a real hypersurface in a complex space form Mn(c), c ≠ 0. In this paper we prove that if the structure tensor field is Codazzi type, then M is a Hopf hypersurface. We characterize such Hopf hypersurfaces of Mn(c).

• The Pure and Applied Mathematics
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• v.28 no.3
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• pp.247-252
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• 2021

Let M be a real hypersurface in a complex space form M_n(c), c ≠ 0. In this paper, we prove that if (∇_Xϕ)Y + (∇_Yϕ)X = 0 holds on M, then M is a Hopf hypersurface, where ϕ is the tangential projection of the complex structure of M_n(c). We characterize such Hopf hypersurfaces of M_n(c).

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.141-151
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• 2002

Let X and Y be real Banach spaces and $\varepsilon$, p $\geq$ 0. A mapping T between X and Y is called an ($\varepsilon$, p)-isometry if ｜∥T(x)-T(y)∥-∥x-y∥｜$\leq$ $\varepsilon$∥x-y∥$^{p}$ for x, y$\in$X. Let H be a real Hilbert space and T : H longrightarrow H an ($\varepsilon$, p)-isometry with T(0) = 0. If p$\neq$1 is a nonnegative number, then there exists a unique isometry I : H longrightarrow H such that ∥T(x)-I(y)∥$\leq$ C($\varepsilon$)(∥x∥$^{ 1+p)/2}$+∥x∥$^{p}$ ) for all x$\in$H, where C($\varepsilon$) longrightarrow 0 as $\varepsilon$ longrightarrow 0.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.479-491
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• 2013

Let M be a smooth real hypersurface in complex space of dimension $n$, $n{\geq}3$, and assume that the Levi-form at $z_0$ on M has at least $(q+1)$-positive eigenvalues, $1{\leq}q{\leq}n-2$. We estimate solutions of the local $\bar{\partial}$-closed extension problem near $z_0$ for $(p,q)$-forms in Sobolev spaces. Using this result, we estimate the local solution of tangential Cauchy-Riemann equation near $z_0$ in Sobolev spaces.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.7-27
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• 2015

Kuneth formula is to compute (co)-homology of $A{\otimes}B$ for known (co)-homology of the complexes A and B. In the ordinary case, this is done by using elementary homological methods in an abelian category. However, when we consider the bounded cochain complex with values in $\mathbb{R}$ and its structure as a real Banach space, the techniques of homological algebra for constructing K$\ddot{u}$nneth type formulas on it are not effective. The most notable facts are the image of a morphism of Banach spaces is not necessarily closed, and also the closed summand of a Banach space need not be a topological direct summand. The main goal of this paper is to construct the theory of K$\ddot{u}$nneth type formula on bounded cohomology with real coefficients in the suitable category of Banach spaces with some restricted conditions.