• 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.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.233-244
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• 2017

Differential subordination and superordination results associated with a generalized Hurwitz-Lerch Zeta function in the open unit disk are obtained by investigating appropriate classes of admissible functions. In particular some inequalities for generalized Hurwitz-Lerch Zeta function are obtained.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1361-1365
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• 2003

There are two Clausius inequalities. One involves the temperature of external reservoir and the other involves the temperature at the system boundary. It is shown that the former Clausius inequality can be established from a direct application of the proposition regarding the efficiency of a Carnot cycle based on an apparatus with two reservoirs. A different apparatus which also has two thermal reservoirs is utilized to compare the cyclic integral of the former inequality with that of the latter, resulting in the proof of the latter inequality.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.399-410
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• 2010

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.137-160
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• 2006

We describe the weight functions for which Hardy's inequality of nonincreasing functions is satisfied. Further we characterize the pairs of weight functions $(w,v)$ for which the Laplace transform $\mathcal{L}f(x)={\int}^{\infty}_0e^{-xy}f(y)dy$, with monotone function $f$, is bounded from the weighted Lebesgue space $L^p(w)$ to $L^q(v)$.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.495-502
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• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.161-172
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• 2016

In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.279-295
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• 2019

In this paper, using local fractional integrals on fractal sets $R^{\alpha}(0<{\alpha}{\leq}1)$ of real line numbers, we establish new some inequalities of Simpson's type based on generalized convexity.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.653-665
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• 2020

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.401-418
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• 2021

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some $L^{\frac{n}{2}}$-integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.