• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.843-854
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• 2020

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.131-143
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• 2004

Let Ε and F be locally convex spaces over C. We assume that Ε is a nuclear space and F is a Banach space. Let f be a holomorphic mapping from Ε into F. Then we show that f is of uniformly bounded type if and only if, for an arbitrary locally convex space G containing Ε as a closed subspace, f can be extended to a holomorphic mapping from G into F.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1163-1173
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• 2019

In this article, we deduced some new inequalities related to hyper-Bessel function. By using these inequalities we will find some sufficient conditions under which certain families of integral operators are convex in the open unit disc. Some applications related to these results are also the part of our investigation.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.6
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• pp.257-266
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• 2015

There is no polynomial-time algorithm that can be obtain the optimal solution for economic load dispatch problem with non-convex fuel cost functions. Therefore, electrical field uses quadratic fuel cost function unavoidably. This paper proposes a valve-point optimization (VPO) algorithm for economic load dispatch problem with non-convex fuel cost functions. This algorithm sets the initial values to maximum powers $P_i{\leftarrow}P_i^{max}$ for each generator. It then reduces the generation power of generator i with an average power cost of $_{max}\bar{c}_i$ to a valve point power $P_{ik}$. The proposed algorithm has been found to perform better than the extant heuristic methods when applied to 13 and 40-generator benchmark data. This paper consequently proves that the optimal solution to economic load dispatch problem with non-convex fuel cost functions converges to the valve-point power of each generator.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.409-421
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• 2018

Let X be a complex manifold of dimension n $n{\geqslant}2$ and let ${\Omega}{\Subset}X$ be a weakly q-convex domain with smooth boundary. Assume that E is a holomorphic line bundle over X and $E^{{\otimes}m}$ is the m-times tensor product of E for positive integer m. If there exists a strongly plurisubharmonic function on a neighborhood of $b{\Omega}$, then we solve the ${\bar{\partial}}$-problem with support condition in ${\Omega}$ for forms of type (r, s), $s{\geqslant}q$ with values in $E^{{\otimes}m}$. Moreover, the solvability of the ${\bar{\partial}}_b$-problem on boundaries of weakly q-convex domains with smooth boundary in $K{\ddot{a}}hler$ manifolds are given. Furthermore, we shall establish an extension theorem for the ${\bar{\partial}}_b$-closed forms.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.235-247
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• 2012

We study sufficient conditions for function algebras generated by four smooth functions on a small closed bidisk near the origin in $\mathbb{C}$ to coincide with the space of continuous functions on the bidisk. This problem in one dimension has been studied by De Paepe and the second name author.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.193-200
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• 1992

This paper uses a piecewise ratonal cubic interpolant to solve the problem of shape preserving interpolation for plane curves; scalar curves are also considered as a special case. The results derived here are actually the extensions of the convexity preserving results of Delbourgo and Gregory [Delbourgo and Gregory'85] who developed a $C^{1}$ shape preserving interpolation scheme for scalar curves using the same piecewise rational function. They derived the ocnstraints, on the shape parameters occuring in the rational function under discussion, to make the interpolant preserve the convex shape of the data. This paper begins with some preliminaries about the rational cubic interpolant. The constraints consistent with convex data, are derived in Sections 3. These constraints are dependent on the tangent vectors. The description of the tangent vectors, which are consistent and dependent on the given data, is made in Section 4. the convexity preserving results are explained with examples in Section 5.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.317-323
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• 2015

The purpose of the present paper is to study certain radii problems for the function $$f(z)=\[{\frac{z^{1-{\gamma}}}{{\gamma}+{\beta}}}\(z^{\gamma}[D^nF(z)]^{\beta}\)^{\prime}\]^{1/{\beta}}$$, where ${\beta}$ is a positive real number, ${\gamma}$ is a complex number such that ${\gamma}+{\beta}{\neq}0$ and the function F(z) varies various subclasses of analytic functions with fixed second coefficients. Relevant connections of the results presented herewith various well-known results are briefly indicated.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1279-1287
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• 2019

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient ${\rho}$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient ${\rho}$-Einstein soliton with convex Einstein potential possesses non-negative scalar curvature. We have also deduced a sufficient condition for a Riemannian manifold to be compact which satisfies almost ${\eta}$-Ricci soliton.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.445-454
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• 2022

Using the concept of the strong differential subordination introduced in [2], we find conditions on the functions θ, 𝜑, G, F such that the first order strong subordination θ(p(z)) + $\frac{G(\xi)}{\xi}$zp'(z)𝜑(p(z)) ≺≺ θ(q(z)) + F(z)q'(z)𝜑(q(z), implies p(z) ≺ q(z), where p(z), q(z) are analytic functions in the open unit disk 𝔻 with p(0) = q(0). Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in [1].