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Ornek, Bulent Nafi Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2
In this paper, a boundary version of the Schwarz lemma is investigated. We take into consideration a function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$ holomorphic in the unit disc and $\|\frac{f(z)}{{\lambda}f(z)+(1-{\lambda})z}-{\alpha}\|$ < ${\alpha}$ for ${\mid}z{\mid}$ < 1, where $\frac{1}{2}$ < ${\alpha}$ ${\leq}{\frac{1}{1+{\lambda}}}$, $0{\leq}{\lambda}$ < 1. If we know the second and the third coefficient in the expansion of the function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$, then we can obtain more general results on the angular derivatives of certain holomorphic function on the unit disc at boundary by taking into account $c_{p+1}$, $c_{p+2}$ and zeros of f(z) - z. We obtain a sharp lower bound of ${\mid}f^{\prime}(b){\mid}$ at the point b, where ${\mid}b{\mid}=1$.
A SHARP SCHWARZ AND CARATHÉODORY INEQUALITY ON THE BOUNDARY
Ornek, Bulent Nafi Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.1
In this paper, a boundary version of the Schwarz and Carath$\acute{e}$odory inequality are investigated. New inequalities of the Carath$\acute{e}$odory's inequality and Schwarz lemma at boundary are obtained by taking into account zeros of f(z) function which are different from zero. The sharpness of these inequalities is also proved.
SHARPENED FORMS OF THE SCHWARZ LEMMA ON THE BOUNDARY
Ornek, Bulent Nafi Korean Mathematical Society 2013 대한수학회보 Vol.50 No.6
In this paper, a boundary version of the Schwarz lemma is investigated. We obtain more general results at the boundary. Also, new inequalities of the Schwarz lemma at boundary is obtained and the sharpness of these inequalities is proved.
SOME RESULTS OF THE CARATHÉODORY'S INEQUALITY AT THE BOUNDARY
Ornek, Bulent Nafi Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.4
In this paper, a boundary version of the $Carath{\acute{e}}odory^{\prime}s$ inequality is investigated. We shall give an estimate below ${\mid}f^{\prime}(b){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these estimates is also proved.
INEQUALITIES FOR THE NON-TANGENTIAL DERIVATIVE AT THE BOUNDARY FOR HOLOMORPHIC FUNCTION
Ornek, Bulent Nafi Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.3
In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}$ defined in the unit disc, with ${\Re}\(\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}\)$ > ${\beta}$, $0{\leq}{\beta}$ < 1, $0{\leq}{\lambda}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ${\xi}$, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.
Psychological Health Problems Among Adolescent Workers and Associated Factors in Istanbul, Turkey
Ornek, Ozlem Koseoglu,Esin, Melek Nihal Occupational Safety and Health Research Institute 2018 Safety and health at work Vol.9 No.1
Background: Work and work environment have a critical influence on adolescent workers' health. They are subjected to more risks than adults. The aim of this study is to examine psychological health outcomes in adolescent workers in the areas of depression, somatization, anxiety, hostility, and negative self-concept, and to investigate any related factors. Methods: This is a descriptive and cross-sectional study. Research samples were collected from adolescent workers between 15 and 18 years old attending a 1-day mandatory education course at vocational training centers, working 5 days per week in small enterprises. Data were collected using the following instruments: Brief Symptom Inventory, Multidimensional Scale of Perceived Social Support, and Descriptive Characteristics of Children's Assessment Form. Results: The investigation covers 837 young workers, of whom 675 were males and 162 were females. The majority of the families had low incomes (68.1%). Overall, 33.5% of the adolescents had been hospitalized because of health problems. Their average weekly working hours were $78.1{\pm}10.7$. Almost 50% of adolescent workers scored above the mean average in the Brief Symptom Inventory, indicating serious pschological health symptoms. Those who scored high for hostility, depression, negative self-concept, anxiety, and somatization were between 45.4% and 48.9% of the sample. Logistic regression analysis was conducted to determine the underlying factors: a perception of "feeling very bad" health conditions was 2.07-fold whereas the rate of "no annual leave" was 0.73-fold, and both were found to be effective on psychological problems. Conclusion: In this study, it seems likely that psychological health problems are the result of multiple adverse factors including working conditions, annual leave, and health considerations.
A SHARP CARATHÉODORY'S INEQUALITY ON THE BOUNDARY
Ornek, Bulent Nafi Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.3
In this paper, a generalized boundary version of $Carath{\acute{e}}odory^{\prime}s$ inequality for holomorphic function satisfying $f(z)= f(0)+a_pz^p+{\cdots}$, and ${\Re}f(z){\leq}A$ for ${\mid}z{\mid}$<1 is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime}(c)$ at the point c with ${\Re}f(c)=A$. The sharpness of these estimates is also proved.
SOME REMARKS OF THE CARATHÉODORY'S INEQUALITY ON THE RIGHT HALF PLANE
Ornek, Bulent Nafi Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.1
In this paper, a boundary version of Carathéodory's inequality on the right half plane for p-valent is investigated. Let Z(s) = 1+c<sub>p</sub> (s - 1)<sup>p</sup> +c<sub>p+1</sub> (s - 1)<sup>p+1</sup> +⋯ be an analytic function in the right half plane with ℜZ(s) ≤ A (A > 1) for ℜs ≥ 0. We derive inequalities for the modulus of Z(s) function, |Z'(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and finally, the sharpness of these inequalities is proved.
An Overview of Conceptual Change Models: Some Cases from Physics
Funda Ornek 대한사고개발학회 2009 The International Journal of Creativity & Problem Vol.19 No.2
As Halloun & Hestenes (1985) have shown, many students come to college physics courses with misconceptions and leave with them as well. In this review, it is attempted to explain the nature of conceptual change models of Posner et al. (1982), diSessa (1993), Vosniadou (1992, 1994, and 2002), and Chi et al. (1994) that take place in the construction of new knowledge of physics and physical science. It is discussed that conceptual change models can lead to a framework for improving science teaching and construction of new knowledge in science. In addition, some examples from physics are given to elucidate these conceptual change models.
On bounds for the derivative of analytic functions at the boundary
Bulent Nafi Ornek,Tugba Akyel 강원경기수학회 2021 한국수학논문집 Vol.29 No.4
In this paper, we obtain a new boundary version of the Schwarz lemma for analytic function. We give sharp upper bounds for $\left\vert f^{\prime}(0)\right\vert $ and sharp lower bounds for $\left\vert f^{\prime}(c)\right\vert $ with $c\in \partial D=\left\{ z:\left\vert z\right\vert=1\right\} $. Thus we present some new inequalities for analytic functions. Also, we estimate the modulus of the angular derivative of the function $f(z) $ from below according to the second Taylor coefficients of $f$ about $z=0$ and $z=z_{0}\neq 0.$ Thanks to these inequalities, we see the relation between $\vert f^{\prime }(0)\vert$ and $\Re f(0).$ Similarly, we see the relation between $\Re f(0)$ and $\vert f^{\prime }(c)\vert$ for some $c\in\partial D.$ The sharpness of these inequalities is also proved.