• Honam Mathematical Journal
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• v.23 no.1
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• pp.41-50
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• 2001

This paper concerns with the subclass of normalized analytic function f in D = {z : |z| < 1}, namely a ${\delta}$-convex function in a sector. This subclass is denoted by ${\Delta}({\delta})$, where ${\delta}$ is a real positive. Given $0<{\beta}{\leq}1$ then for $z{\in}D$, the exact ${\alpha}({\beta},\;{\delta})$ is found such that $f{\in}{\Delta}({\delta})$ implies $f{\in}S^*({\beta})$, where $S^*({\beta})$ is starlike of order ${\beta}$ in a sector. This work is a more general version of the result of Nunokawa and Thomas [11].

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.671-681
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• 2014

In this paper, we consider general Beta operators, which is a general sequence of integral type operators including Beta function. We study the King type Beta operators which preserves the third test function $x^2$. We obtain some approximation properties, which include rate of convergence and statistical convergence. Finally, we show how to reach best estimation by these operators.

• International journal of advanced smart convergence
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• v.4 no.1
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• pp.35-39
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• 2015

This study was presented the small action by the budge sonance function. An estimation of budge sonance function was acquired displacements across all condition with a variation of small action. The budge sonance function was to be indicated to express the flow rate of body motion. Their function was suggested an issue of the action condition by budge sonance. This system was proposed a combination of the body motion and small action. The acquired sonance signal was to render the small action of body motion with budge sonance function. The analysis of budge function was generally realized a variation from displacements on the fast body motion. Budge sonance signal of action that vision condition was acquired to a variation of the $Vi-{\beta}_{AVG}$ with $(-4.954){\pm}(-5.42)$ units, that vestibular condition was acquired to a variation for the $Ve-{\beta}_{AVG}$ with $(-2.288){\pm}0.212$ units, that somatosensory condition was acquired to a variation for the $So-{\beta}_{AVG}$ with $(-0.47){\pm}0.511$ units, that CNS condition was acquired to a variation for the $C-{\beta}_{AVG}$ with $(-0.171){\pm}(-0.012)$ units. Budge sonance function was proposed the small action from axial action on body control. We know a body motion response from axial action was not only variation of budge sonance, but also body motion of fast body motion.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.2
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• pp.179-187
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• 2016

This study was conducted to identify the factors that affect the nursing performance. These factors are general characteristics, mentoring function and organizational citizenship behavior. A survey was conducted on 163 nurses working for general hospitals in South Korea from December 2 - 30, 2015. The data was analyzed using the SPSS WIN 21.0 program to analyze the descriptive statistics, independent T-test, ANOVA, Scheffe test, Pearson's correlation, and multiple regression. The factors affecting the subject's nursing performance were altruism (${\beta}=.46$, p<.001), courtesy (${\beta}=.12$, p=.047), belonging to the sub areas of the organizational citizenship behaviors, role modeling function (${\beta}=.31$, p=.001), career develop functions (${\beta}=-.22$, p=.018), belonging to the sub areas of the mentoring function, and position (${\beta}=.24$, p<.001). The results of this study are expected to provide basic data to improve the nursing performance.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.229-241
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• 1997

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.769-780
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. Very recently, Choi [6] presented explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function. In the present sequel to the investigation [6], we evaluate the log-sine and log-cosine integrals involved in more complicated integrands than those in [6], by also using the Beta function.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.137-146
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.507-522
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• 2019

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al. [19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.13-21
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• 2019

In the present research paper, we introduce a further extension of Hurwitz-Lerch zeta function by using the generalized extended Beta function defined by Parmar et al.. We investigate its integral representations, Mellin transform, generating functions and differential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.