• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.575-585
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• 1996

Recently, existence theorems of coupled fixed points for mixed monotone operators have been considered by several authors (see [1]-[3], [6]). In this paper, we are continuously going to study the existence problems of coupled fixed points for two more general classes of mixed monotone operators. As an application, we utilize our main results to show thee existence of coupled fixed points for a class of non-linear integral equations.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Journal of the Korean Society of Physical Medicine
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• v.9 no.2
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• pp.233-242
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• 2014

PURPOSE: The purpose of this study was to determine the correlation between the hip adductor muscles and abdominal muscles during bridge exercise. METHOD: Participants who met the criteria for this study(n=36) were divided into the three groups. The first experimental group performed normal bridge exercises and the second group performed bridge exercises with the contraction of the hip adductor muscles and the control group didn't perform any exercise. Transversus abdominis muscle thickness was measured by ultrasound imaging with a special transducer head device, at pre exercise, after 2 weeks, 4 weeks, and 6 weeks. RESULT: Data were analyzed using repeated ANOVA with the level of significance set at ${\alpha}=.05$. Transversus abdominis muscle thickness was influenced by contraction of the hip adductor muscles during bridge exercise in people without lower back pain. Compared with normal bridge exercise, transversus abdominis muscle thickness significantly increased in thickness during bridge exercise with contraction of the hip adductor muscles(p<.05). CONCLUSION: The results from this study showed that contraction of the hip adductor muscles during bridge exercise increased change in the transversus abdominis muscle thickness. These results can be a good source to prevent low back pain due to hip adductor weakness. Therefore, inducing activation of hip adductor with abdominal stabilizing exercise is more effective in patients with low back pain.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Physical Therapy Korea
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• v.24 no.1
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• pp.71-78
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• 2017

Background: Muscle weakness and impaired trunk muscle control are common in stroke patients. The bridging exercise (BE) is generally used for trunk stabilization and improving the overall function of stroke patients. The effectiveness of the BE with hip adductor contraction (BEHA) in facilitating trunk muscle activation has been well studied in healthy adults. However, the impact of BEHA in sub-acute stroke patients has not yet been investigated. Objects: The purpose of this study was to determine the effects of BEHA on the electromyography (EMG) activities and the asymmetry of the rectus abdominis (RA), external oblique (EO) and internal oblique (IO) abdominal muscles. Methods: Twenty participants with sub-acute stroke (11 males and 9 females) were recruited. Each participant was asked to perform bridging exercises for five seconds under three different conditions: BE in a neutral position (BEN), BEHA with a large ball (BEHAL) and BEHA with a small ball (BEHAS). The EMG amplitudes of the bilateral RA, EO and IO and the asymmetry of the EMG activity between the sound and affected sides were compared among the conditions. The significance level was set at ${\alpha}=.05$. Results: The EMG activities of RA, EO and IO were significantly greater during BEHAL and BEHAS than during BEN (p<.05); the asymmetry of the RA, EO and IO decreased significantly during BEHAL and BEHAS compared to BEN (p<.05). However, no measured variables showed any significant differences between BEHAL and BEHAS (p>.05). Conclusion: This study compared the EMG activities of the RA, EO and IO on both sides and the asymmetry of the RA, EO and IO during BEN, BEHAL and BEHAS. Our findings suggest that BEHA was more effective for individuals with hemiplegic stroke at facilitating and normalizing abdominal muscle control than BEN.

• The Journal of Advanced Prosthodontics
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• v.9 no.3
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• pp.182-187
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• 2017

PURPOSE. Vinyl polyether silicone (VPES) has a different composition from other elastomeric impression materials as it combines vinyl polysiloxane (VPS) and polyether (PE). Therefore, it is important to study its properties and behavior under different test conditions. This study investigated the dimensional stability of 5 VPES consistencies when stored for up to 2 weeks, with and without using a standard disinfection procedure. MATERIALS AND METHODS. 40 discs of each VPES consistency (total 200) were made using a stainless steel die and ring as described by ANSI /ADA specification No. 19. 20 discs of each material were immersed in a 2.5% buffered glutaraldehyde solution for 30 minutes. Dimensional stability measurements were calculated immediately after fabrication and repeated on the same discs after 7 and 14 days of storage. The data was analyzed using two-way ANOVA with a significance level set at ${\alpha}=0.05$. RESULTS. The discs mean contraction was below 0.5% at all test times ranging from $0.200{\pm}0.014$ to $0.325{\pm}0.007$. Repeated measures ANOVA showed a statistically significant difference after 2-week storage between the disinfected and non-disinfected groups (P < .001). Although there was no statistically significant difference between the materials at the time of fabrication, the contraction of the materials increased with storage for 1 and 2 weeks. CONCLUSION. The dimensional changes of VPES impression discs after disinfection and prolonged storage complied with ANSI/ADA standard. The tested VPES impression materials were dimensionally stable for clinical use after disinfection for 30 minutes in glutaraldehyde and storage for up to 2 weeks.

• Physical Therapy Korea
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• v.19 no.3
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• pp.1-10
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• 2012

The aim of this study is to compare measurements of abdominal muscle thickness using ultrasonography imaging (USI) to those using a special transducer head device, during five different trunk stabilization exercises, ultimately to determine which exercise led to the greatest muscle thickness. Thirty eight healthy subjects participated in this cross-sectional study. The five types of trunk stabilization - i.e., a sit-up on the supine, an upper and lower extremity raise with quadruped on the prone, a leg raise in sitting on the ball, trunk rolling on the ball, and balance using sling on the prone position - were each performed with an abdominal draw. The thickness of the abdominal muscle - including the transverse abdominal (TrA), internal oblique (IO), and external oblique (EO) - was measured by USI with a special transducer head device, at rest and then at contraction in each position. Data were analyzed using one-way repeated ANOVA with the level of significance set at ${\alpha}$=.05. The results were as follows: 1) the TrA thickness was statistically significant (p<.05), whereas the IO and EO thicknesses were not (p>.05); 2) among the five types of trunk stabilization, TrA thickness significantly increased with the balance using a sling in the prone position, (p<.05), whereas no significant difference was noted for the four types of trunk stabilization (p>.05); 3) reliability data showed that there was a high degree of consistency among the measurements taken using the special transducer head device (ICC=.92). In conclusion, the balance using a sling in the prone position was more effective than any of the four other types of trunk stabilization in increasing TrA thickness in healthy subjects.