• Annals of Rehabilitation Medicine
• /
• 제42권6호
• /
• pp.863-871
• /
• 2018

Objective To evaluate the association between progression of curvature of scoliosis, and correction for functional component in patients with juvenile idiopathic scoliosis (JIS). Methods We retrospectively reviewed medical data of patients prescribed custom molded foot orthosis (FO) to correct inequality of RCSPA (resting calcaneal stance position angle), and chose 52 patients (26 females, 26 males) with Cobb angle ${\geq}10^{\circ}$ in radiology and uneven pelvic level at iliac crest by different RCSPA (${\geq}3^{\circ}$) as a factor of functional scoliosis. They had different hump angle ${\geq}5^{\circ}$ in forward bending test, for idiopathic scoliosis component. Their mean age and mean period of wearing FO were $79.5{\pm}10.6months$ and $18.6{\pm}0.70months$. Results Cobb angle was reduced from $22.03^{\circ}{\pm}4.39^{\circ}$ initially to $18.86^{\circ}{\pm}7.53^{\circ}$ after wearing FO. Pelvis height difference and RCSPA difference, were reduced from $1.07{\pm}0.25cm$ initially to $0.60{\pm}0.36$, and from $4.25^{\circ}{\pm}0.71^{\circ}$ initially to $1.71^{\circ}{\pm}0.75^{\circ}$ (p<0.01). Cobb angle improved most in 9 months. However, there was no significant improvement for those with more than $25^{\circ}$ of Cobb angle initially. Mean Cobb angle improved in all age groups, but patients less than 6 years had clinically significant improvement of more than $5^{\circ}$. Conclusion JIS can have functional components, which should be identified and managed. Foot orthosis is useful in correcting functional factors, in the case of pelvic inequality caused by different RCSPA, for patients with juvenile idiopathic scoliosis.

• 충청수학회지
• /
• 제20권2호
• /
• pp.173-182
• /
• 2007

In this paper, we prove the Cauchy-Rassias stability of derivations on quasi-Banach algebras associated to the Cauchy functional equation and the Jensen functional equation. We use the Cauchy-Rassias inequality that was first introduced by Th. M. Rassias in the paper "On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300".

• 대한수학회지
• /
• 제49권5호
• /
• pp.881-891
• /
• 2012

In this paper we investigate the approximate controllability for the following nonlinear functional differential control problem: $$x^{\prime}(t)+Ax(t)+{\partial}{\phi}(x(t)){\ni}f(t,x(t))+h(t)$$ which is governed by the variational inequality problem with nonlinear terms.

• 대한수학회보
• /
• 제48권4호
• /
• pp.725-736
• /
• 2011

By using the Lyapunov functional method, stochastic analysis, and LMI (linear matrix inequality) approach, the mean square exponential stability of an equilibrium solution of uncertain stochastic Hopfield neural networks with delayed is presented. The proposed result generalizes and improves previous work. An illustrative example is also given to demonstrate the effectiveness of the proposed result.

• Communications for Statistical Applications and Methods
• /
• 제6권1호
• /
• pp.261-266
• /
• 1999

We present a geometric interpretation of Chebyshev type inequalities. This uses a simple diagram which illustrates the functional bound for the indicator function of the event whose probability we want to assess. We also give a geometric interpretation of the inequalities in terms of volume in a Euclidean space of appropriate dimension. Markov's inequality and Chebyshev's inequality are treated in more detail.

• Nonlinear Functional Analysis and Applications
• /
• 제26권4호
• /
• pp.781-792
• /
• 2021

In this paper, we study well-posed problems and variational inequalities in locally convex Hausdorff topological vector spaces. The necessary and sufficient conditions are obtained for the existence of solutions of variational inequality problems and quasi variational inequalities even when the underlying set K is not convex. In certain cases, solutions obtained are not unique. Moreover, counter examples are also presented for the authenticity of the main results.

• Nonlinear Functional Analysis and Applications
• /
• 제27권4호
• /
• pp.797-805
• /
• 2022

Let P(z) be a polynomial of degree n. A well-known inequality due to S. Bernstein states that if P ∈ P_n, then $$\max_{{\mid}z{\mid}=1}\,{\mid}P^{\prime}(z){\mid}\,{\leq}n\,\max_{{\mid}z{\mid}=1}\,{\mid}P(z){\mid}$$. In this paper, we establish some extensions and refinements of the above inequality to polar derivative and some other well-known inequalities concerning the polynomials and their ordinary derivatives.

• Nonlinear Functional Analysis and Applications
• /
• 제28권3호
• /
• pp.647-657
• /
• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• Nonlinear Functional Analysis and Applications
• /
• 제28권3호
• /
• pp.813-830
• /
• 2023

Let p(z) be a polynomial of degree n having no zero in |z| < 1. In this paper, by involving some coefficients of the polynomial, we prove an inequality that not only improves as well as generalizes the well-known result proved by Rivlin but also has some interesting consequences.

• Nonlinear Functional Analysis and Applications
• /
• 제28권2호
• /
• pp.421-437
• /
• 2023

Let p(z) be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then Malik [12] obtained the following inequality: $${_{max \atop {\mid}z{\mid}=1}{\mid}p{\prime}(z){\mid}{\leq}{\frac{n}{1+k}}{_{max \atop {\mid}z{\mid}=1}{\mid}p(z){\mid}.$$ In this paper, we shall first improve as well as generalize the above inequality. Further, we also improve the bounds of two known inequalities obtained by Govil et al. [8].