• PNF and Movement
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• 제12권4호
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• pp.201-207
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• 2014

Purpose: The purpose of this study was functional leg length inequality effect on COP(Center Of Pressure) and LOS(limits Of Stability) and EMG activation. Methods: The participants were consisted of fourteen. Subjects were distributed 2 groups; control group, leg length inequality ${\leq}3mm$, n=8), experimental group(leg length inequality${\geq}10mm$, n=8). The participants were measured leg length wearing comfortable clothes through tape measure method(TMM). All subjects was measured COP(Center Of Pressure), LOS(limits of stability) using by Balance Trainer BT4(HUR, Finland). Results: The results COP was not exist statistical significant differences(p>0.05). LOS was not exist statistical significant difference(p>0.05). Conclusion: The results was not statistical significant differences COP and LOS depending on Leg Length Inequality. But between experimental group and comparison group was exist mean differences on COP, LOS(COP:Ex.>Com, LOS:Ex.

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

• The Journal of Korean Physical Therapy
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• 제21권1호
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• pp.49-55
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• 2009

Purpose: The purpose of this study was to evaluate influence of contract-relax exercise on functional leg length inequality (FLLI) and muscle activity. Methods: The subjects were consisted of 40 healthy adults who had FLLI of which degree was at least 10mm. All subjects were randomly assigned to two groups : Contract-Relax Exercise (CRE) group (n=20), control group (n=20). The experimental group underwent CRE for 3 times a week for 4 weeks. Myosystem 1200 was used to measure the activity of rectus femoris and hamstring muscle. The tape measure method was used to measure FLLI. Statistical analysis was used repeated ANOVA know comparison of period, independent T-est know comparison of experiment group and control group. Results: All measurements for each subject took the following test : pre-test, post-test in 2 weeks, post-test in 4 weeks. The FLLI of the experimental group was significantly reduced according to within intervention period (p<0.05). Rectus femoris and hamstring muscle activity of the experimental group was significantly increased (p<0.05). Conclusion: The CRE can reduce FLLI and increase rectus femoris and hamstring muscle activity. Various contract-relax exercise for reduced of FLLI and the methods should be customized for the patients.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.373-380
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• 2021

If $p(z)={\sum\limits_{{\nu}=0}^{n}}a_{\nu}z^{\nu}$ is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then Govil [3] proved that $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{n}{k^n+k^{n-1}}}\;{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. In this paper, by involving certain coefficients of p(z), we not only improve the above inequality but also improve a result proved by Dewan and Mir [2].

• 충청수학회지
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• 제20권2호
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• pp.173-182
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• 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".

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.323-329
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• 2022

Let $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ be a polynomial of degree n and $p^{\prime}(z)$ its derivative. If $\max\limits_{{\mid}z{\mid}=r}{\mid}p(z){\mid}$ is denoted by M(p, r). If p(z) has all its zeros on |z| = k, k ≤ 1, then it was shown by Govil [3] that $$M(p^{\prime},\;1){\leq}\frac{n}{k^n+k^{n-1}}M(p,\;1)$$. In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.647-657
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• 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
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• 제28권3호
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• pp.813-830
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• 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
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• 제26권2호
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• pp.331-345
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• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.141-148
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• 2022

Let p(z) be a polynomial of degree n having no zero in |z| < k, k ≤ 1, then Govil proved $$\max_{{\mid}z{\mid}=1}{\mid}p^{\prime}(z){\mid}{\leq}{\frac{n}{1+k^n}}\max_{{\mid}z{\mid}=1}{\mid}p(z){\mid}$$, provided |p'(z)| and |q'(z)| attain their maximal at the same point on the circle |z| = 1, where $$q(z)=z^n{\overline{p(\frac{1}{\overline{z}})}}$$. In this paper, we extend the above inequality to polar derivative of a polynomial. Further, we also prove an improved version of above inequality into polar derivative.