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SOME REMARKS ON THE SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA
Akyel, Tugba The Kangwon-Kyungki Mathematical Society 2021 한국수학논문집 Vol.29 No.2
In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Rogosinski's lemma, Subordination principle and Jack's lemma were used.
SOME REMARKS FOR λ-SPIRALLIKE FUNCTION OF COMPLEX ORDER AT THE BOUNDARY OF THE UNIT DISC
Akyel, Tugba Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.4
We consider a different version of Schwarz Lemma for λ-spirallike function of complex order at the boundary of the unit disc D. We estimate the modulus of the angular derivative of the function $\frac{zf^{\prime}(z)}{f(z)}$ from below for λ-spirallike function f(z) of complex order at the boundary of the unit disc D by taking into account the zeros of the function f(z)-z which are different from zero. We also estimate the same function with the second derivatives of the function f at the points z = 0 and z = z<sub>0</sub> ≠ 0. We show the sharpness of these estimates and present examples.
A SHARP SCHWARZ LEMMA AT THE BOUNDARY
Tuğba AKYEL,Bülent Nafi ÖRNEK 한국수학교육학회 2015 純粹 및 應用數學 Vol.22 No.3
In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z)=a+c_{p}z^{p}+c_{p+1}z^{p+1}+... defined in the unit disc satisfying |f(z)-1|<1, where 0 < a < 2, we estimate a module of angular
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.
AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY
Bülent Nafi ÖRNEK,Tuğba AKYEL 한국수학교육학회 2016 純粹 및 應用數學 Vol.23 No.1
In this paper, a boundary version of the Schwarz lemma for the holomrophic function satisfying f(a)=b, |a|<1, b∈ℂ and ℜf(z)>α, 0≤α<|b| for |z|<1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c)=α. The sharpness of these inequalities is also proved.
Estimates for a Certain Subclass of Holomorphic Functions
BÜLENT NAFI ÖRNEK,TUĞBA AKYEL 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.2
In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to N(α) is investigated. For the function f(z) = z + c2z2 + c3z3 + ... which is defined in the unit disc where f(z) ∈ N(α), we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with f(b) = 1 b b ∫ 0 f(t)dt. The sharpness of these inequalities is also proved.
Endocan and Non-Dipping Circadian Pattern in Newly Diagnosed Essential Hypertension
Tolga Çimen,Murat Bilgin,Ahmet Akyel,Mehmet Ali Felekoğlu,Ali Nallbani,Şeyda Özdemir,Gönül Erden,Alpaslan Öztürk,Mehmet Doğan,Ekrem Yeter 대한심장학회 2016 Korean Circulation Journal Vol.46 No.6
Background and Objectives: Non-dipper hypertension is frequently accompanied by endothelial dysfunction and activation. Previous studies suggested that endocan may be a novel endothelial dysfunction marker. This study aims to investigate the association between circadian blood pressure (BP) pattern and plasma endocan levels together with high-sensitivity C-reactive protein (hsCRP) in patients with newly diagnosed untreated hypertension. Subjects and Methods: Twenty-four hour ambulatory blood pressure monitoring was recorded in 35 dipper, 35 non-dipper hypertensives and 35 healthy controls. Endocan levels were measured by enzyme-linked immunosorbent assay. Serum levels of hsCRP were also recorded. Results: Despite similar daytime and 24-hour average BP values between dippers and non-dippers, statistically significant high nocturnal BP was accompanied by a non-dipping pattern (Systolic BP: 132±9 vs. 147±11 mmHg; Distolic BP: 80±7 vs. 91±9 mmHg, respectively, p<0.001 for both). Non-dipper patients demonstrated higher endocan levels compared to dippers and normotensives (367 (193-844) pg/mL, 254 (182-512) pg/mL and 237 (141-314) pg/ml, respectively, p<0.001). HsCRP levels were significantly higher in non-dippers than the other groups (p=0.013). In a multivariate logistic regression analysis, endocan (p=0.021) and hsCRP (p=0.044) were independently associated with a non-dipping pattern. Conclusion: Elevated endocan levels were found in non-dipper groups. Endocan and hsCRP were found to be independently associated with a non-dipping pattern. We suggest that elevated levels of endocan in non-dipper hypertensive patients might be associated with a longer duration of exposure to high BP. These results point to the possible future role of endocan in selection of hypertensive patients at higher risk or target organ damage