• Korean Journal of Mathematics
• /
• v.22 no.2
• /
• pp.317-323
• /
• 2014

In this paper, we solve the additive functional inequality $${\parallel}f(x)+f(y)+f(z){\parallel}{\leq}{\parallel}{\rho}f(s(x+y+z)){\parallel}$$, where s is a nonzero real number and ${\rho}$ is a real number with ${\mid}{\rho}{\mid}$ < 3. Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.2
• /
• pp.149-159
• /
• 2022

In this note, we prove some theorems concerning the stability of functional inequality associated with additive mappings on quasi-𝛽-normed spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.503-514
• /
• 2007

In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies the functional inequality with perturbing term which satisfies certain conditions then there exists a Cauchy additive mapping near the mapping.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.295-306
• /
• 2024

In this work, we investigate the generalized Hyers-Ulam stability of quadratic functional inequality in modular spaces satisfying ∆₂-conditions and Fatou property, and in 𝛽-homogeneous Banach spaces.

• The Journal of Korea CHUNA Manual Medicine
• /
• v.5 no.1
• /
• pp.19-29
• /
• 2004

Objectives : Visual check and X-ray are commonly used by chiropractors to estimate ieg length inequality, This study have three categories: diagnosis for anatomic leg length inequality; difference between anatomic and functional leg length inequality; theraphies for anatomic or functional leg length inequality. Methods : We referred to a PubMed site by using word of 'leg length [JU] J Manipulative Physiol Ther', only items with abstracts. Results : We searched 26 articles in J Manipulative Physiol Ther with the key word-Ieg length. Conclusion : 1. Radiographs were most accurate and commonly used by chiropractors to measure anatomic leg length inequality, clinically wood block, tape measure, visual check are acceptable. 2. There was no article about difference between anatomic and functional leg length inequality. 3. Heel lift was commonly used with conservative theraphy for anatomic leg length Inequality. 4. Chiropractors have not yet proved that the supposed positive effects are a result of a reduction of subluxation, The detection of the manipulative lesion in the sacroiliac joint depends on valid and reliable tests, Because such tests have not been established, the presence of the manipulative lesion remains hypothetical. Great effort is needed to develop, establish and enforce valid and reliable test procedures.

• The Pure and Applied Mathematics
• /
• v.15 no.4
• /
• pp.393-400
• /
• 2008

In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||${\leq}$||f(x+y)+f(z+w)|| in normed modules over a $C^*$-algebra. This is applied to understand homomor-phisms in $C^*$-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||${\leq}$||f(x+y+z+w)||+${\theta}||x||^p||y||^p||z||^p||w||^p$ in real Banach spaces, where ${\theta}$, p are positive real numbers with $4p{\neq}1$.

• The Journal of Korean Physical Therapy
• /
• v.21 no.4
• /
• pp.43-49
• /
• 2009

Purpose: This study examined the dynamic peak plantar pressure under the foot areas in those with a functional leg length inequality. Methods: The dynamic peak plantar pressure under the foot areas in an experimental group with a functional leg length inequality (n=20) and a control group (n=20) was assessed a using the Mat-Scan system (Tekscan, USA). The peak plantar pressure under the hallux, 1st, 2nd, 3-4th and 5th metatarsal head (MTH), mid foot, and heel was measured while the subject was walking on the Mat-Scan system. Results: The experimental group had significantly higher peak plantar pressure under all foot areas when the dynamic peak plantar pressure in the short leg and long leg sides was compared. The control group had a significantly higher peak plantar pressure under the 1st, 2nd, 3-4th, and 5th MTH when the dynamic peak plantar pressure in the short leg and long leg sides were compared. The experimental group showed a significantly larger difference in the dynamic peak plantar pressure under the hallux, 1st, 2nd, 3-4th and 5th MTH, mid foot and heel than the control group. Conclusion: A functional leg length inequality leads to an increase in the weight distribution and dynamic peak plantar pressure in the side of the short leg.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.671-681
• /
• 2013

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(x-y)+f(y-z)+f(z){\parallel}{\leq}{\parallel}f(x){\parallel}$$ in Banach spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.907-913
• /
• 2013

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

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.233-241
• /
• 2010

In this paper, we investigate the following functional inequality $${\parallel}f(\frac{x\;+\;y}{2}\;+\;z)\;+\;f(\frac{x\;+\;y}{2}\;+\;y)\;+\;f(\frac{y\;+\;z}{2}\;+\;x){\parallel\;\leq\;\parallel}2f(x\;+\;y\;+\;z)\parallel$$ in Banach modules over a $C^*$-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a $C^*$-algebra.