• 충청수학회지
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• 제29권1호
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• pp.103-108
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• 2016

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(x_1+x_2)+f(x_2+x_3)+{\cdots}+f(x_n+x_1){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that $2{\leq}t$ < n.

• East Asian mathematical journal
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• 제23권2호
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• pp.229-246
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• 2007

Some inequalities related to the $H{\ddot{o}}lder$ integral inequality and applications for bounding the ${\check{C}}eby{\check{s}}ev$ functional are given.

• 호남수학학술지
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• 제35권2호
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• pp.129-136
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• 2013

Let G be a commutative group which is 2-divisible, $\mathbb{R}$ the set of real numbers and $f,g:G{\rightarrow}\mathbb{R}$. In this article, we investigate bounded solutions of the Pexider-exponential functional inequality ${\mid}f(x+y)-f(x)g(y){\mid}{\leq}{\epsilon}$ for all $x,y{\in}G$.

• 대한물리치료과학회지
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• 제13권1호
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• pp.21-27
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• 2006

The purpose of this study was to identify the above mentioned therapy on the reduction of functional leg length inequality, by the manipulation(Thonpson technique). In 8 patients who have been chronically ill with low back pain and functional leg length inequality, for past 12 weeks, we analyzed and observed the progress of symptom and sign on pelvis(femur head line level, ilium length, ilium rotation), using by X-ray. The results after 12 week treatment, compared with before treatment, were as follows : 1. The improved in femur head line in the manipulation after 12 week treatment was very significant(p<.01) 2. The improved in ilium length in the manipulation after 12 week treatment was very significant(p<.01) 3. The improved in ilium rotation in the manipulation after 12 week treatment was significant(p<.05).

• 대한수학회보
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• 제48권4호
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• pp.853-871
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• 2011

In this paper, we prove the Hyers-Ulam-Rassias stability of the following additive functional inequality: ${\parallel}f(2x)+f(2y)+2f(z){\parallel}\;{\leq}\;{\parallel}2f(x+y+z){\parallel}$ We investigate homomorphisms in proper $CQ^*$-algebras and derivations on proper $CQ^*$-algebras associated with the additive functional inequality (0.1).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.161-170
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• 2018

In this paper, we introduce and solve the following additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) $${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with ${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$ < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) in complex Banach spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권1호
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• pp.21-31
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• 2017

In this paper, we introduce and solve the following additive (${\rho}_1$, ${\rho}_2$)-functional inequality $${\Large{\parallel}}2f(\frac{x+y}{2})-f(x)-f(y){\Large{\parallel}}{\leq}{\parallel}{\rho}_1(f(x+y)+f(x-y)-2f(x)){\parallel}+{\parallel}{\rho}_2(f(x+y)-f(x)-f(y)){\parallel}$$ where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with $\sqrt{2}{\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}<1$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1$, ${\rho}_2$)-functional inequality (1) in complex Banach spaces.

• 대한수학회논문집
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• 제23권3호
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• pp.371-376
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• 2008

In this paper, it is shown that if f satisfies the following functional inequality (0.1) $${\parallel}\sum\limits_{i,j=1}^3\;f{(xi,yj)}{\parallel}{\leq}{\parallel}f(x_1+x_2+x_3,\;y_1+y_2+y_3){\parallel}$$ then f is a bi-additive mapping. We moreover prove that if f satisfies the following functional inequality (0.2) $${\parallel}2\sum\limits_{j=1}^3\;f{(x_j,\;z)}+2\sum\limits_{j=1}^3\;f{(x_j,\;w)-f(\sum\limits_{j=1}^3\;xj,\;z-w)}{\parallel}{\leq}f(\sum\limits_{j=1}^3\;xj,\;z+w){\parallel}$$ then f is an additive-quadratic mapping.

• 한방재활의학과학회지
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• 제21권3호
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• pp.13-20
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• 2011

Objectives : We studied the clinical utility of meridian electromyography for the assessment of erector spinae muscle in functional leg length inequality. Methods : We compared electrical activity between A group with a functional leg length inequality(n=17) and B group(n=23) in dynamic flexion-reextension state during five minutes. We anayzed amplitudes and areas of electrical activity and asymmetry index(AI). Results : 1. The short leg sides were significantly higher electrical activity than the long leg sides in the experimental group and control group(p<0.05). 2. The AI of A group significantly higher than B group(p<0.05). Conclusions : According to above results, there are correlations between erector spinae muscle and functional leg length inequality.

• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.55-66
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• 2018

By making use of the Riemann-Liouville fractional integrals, we establish further results on Chebyshev inequality. Other Steffensen integral results of the weighted Chebyshev functional are also proved. Some classical results of the paper:[ Steffensen's generalization of Chebyshev inequality. J. Math. Inequal., 9(1), (2015).] can be deduced as some special cases.