Yazar "Örnek, Bülent Nafi" seçeneğine göre listele

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    APPLICATIONS OF SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA
    (Korean Soc Mathematical Education, 2020) Aydınoğlu, Selin; Örnek, Bülent Nafi
    In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.
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    APPLICATIONS OF THE JACK'S LEMMA FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA
    (Korean Soc Mathematical Education, 2021) Örnek, Bülent Nafi
    In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered.The results of Rogosinskis lemma and Jacks lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.
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    ON BOUNDS FOR THE DERIVATIVE OF ANALYTIC FUNCTIONS AT THE BOUNDARY
    (Kangwon-Kyungki Mathematical Soc, 2021) Örnek, Bülent Nafi; Akyel, Tuğba
    In this paper, we obtain a new boundary version of the Schwarz lemma for analytic function. We give sharp upper bounds for vertical bar f'(0)vertical bar and sharp lower bounds for vertical bar f'(c)vertical bar with c is an element of partial derivative D -{z:vertical bar z vertical bar - 1}. 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) not equal 0. Thanks to these inequalities, we see the relation between vertical bar f'(0)vertical bar and Rf(0). Similarly, we see the relation between Rf(0) and vertical bar f'(c)vertical bar for some c is an element of partial derivative D. The sharpness of these inequalities is also proved.
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    On the Rigidity Part of Schwarz Lemma
    (Amer Inst Physics, 2019) Akyel, Tuğba; Örnek, Bülent Nafi
    We consider the rigidity part of Schwarz Lemma. Let f be a holomorphic function in the unit disc D and vertical bar Rf(z)vertical bar < 1 for vertical bar z vertical bar < 1. We generalize the rigidity of holomorphic function and provide sufficient conditions on the local behaviour of f near a finite set of boundary points that needs f to be a finite Blaschke product. For a different version of the rigidity theorems of D. Burns-S.Krantz and D. Chelst, we present some more general results in which the bilogaritmic concave majorants are used. The strategy of these results relies on a special version of Phragmen-Lindelof princible and Harnack inequality.
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    On the rigidity part of Schwarz Lemma at the boundary
    (Maltepe Üniversitesi, 2019) Akyel, Tuğba; Örnek, Bülent Nafi
    We consider the rigidity part of Schwarz Lemma. Let f be a holomorphic function in the unit disc D and |?f(z)| < 1 for |z| < 1. We generalize rigidity of holomorphic function and provide sufficient conditions on the local behaviour of f near a finite set of boundary points that needs f to be a finite Blaschke product. For a different version of the rigidity theorems of D. Burns-S.Krantz and D. Chelst, we present some more general results used the bilogaritmic concave majorants. The strategy of these results relies on a special version of Phragmen-Lindel¨of princible and Harnack inequality
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    Sharpened forms for ?-spirallike function of complex order on the boundary
    (Maltepe Üniversitesi, 2021) Örnek, Bülent Nafi
    We present a different version of Schwarz Lemma and estimate the angular derivative of the function z f (z) f(z) from below for ??spirallike function f(z) of complex order at the boundary of the unit disc D by taking into account of the zeros of the function f(z) ? z which are different from zero.
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    Some remarks for a certain class of holomorphic functions at the boundary of the unit disc
    (2019) Akyel, Tuğba; Örnek, Bülent Nafi
    We consider a boundary version of the Schwarz Lemma on a certain class which is denoted by ??(??). Forthe function ??(??) = ?? + ???????? + ????????+. .. which is defined in the unit disc ?? such that the function ??(??)belongs to the class ??(??), we estimate from below the modulus of the angular derivative of the function????'(??)??(??)at the boundary point ?? with ????'(??)??(??)=????????. Moreover, we get the Schwarz Lemma for the class ??(??).We also investigate some inequalities obtained in terms of sharpness.
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    Some results for a certain class of holomorphic functions at the boundary of the unit disc
    (Maltepe Üniversitesi, 2019) Örnek, Bülent Nafi; Akyel, Tuğba
    We consider a version of the boundary Schwarz Lemma on a certain class which is denoted by K(?). For the function f(z) = z + c2z2 + c3z3 + ... defined in the unit disc E such that the function f(z) belongs to the class K(?), we estimate from below the modulus of the angular derivative of the function z f (z) f(z) at the boundary point b with b f (b) f(b) = 1 1+? . Moreover, we get Schwarz Lemma for the class K(?). We also investigate some inequalities obtained in terms of sharpness.