• 제목/요약/키워드: Schwarz Function

검색결과 41건 처리시간 0.033초

TAMED EXHAUSTION FUNCTIONS AND SCHWARZ TYPE LEMMAS FOR ALMOST HERMITIAN MANIFOLDS

  • Weike, Yu
    • 대한수학회보
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    • 제59권6호
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    • pp.1423-1438
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    • 2022
  • In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.

A SHARP SCHWARZ AND CARATHÉODORY INEQUALITY ON THE BOUNDARY

  • Ornek, Bulent Nafi
    • 대한수학회논문집
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    • 제29권1호
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    • pp.75-81
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    • 2014
  • 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.

AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY

  • ORNEK, BULENT NAFI;AKYEL, TUGBA
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제23권1호
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    • pp.61-72
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    • 2016
  • In this paper, a boundary version of the Schwarz lemma for the holom- rophic 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) = a. The sharpness of these inequalities is also proved.

SOME REMARKS ON THE SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA

  • Akyel, Tugba
    • Korean Journal of Mathematics
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    • 제29권2호
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    • pp.293-304
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    • 2021
  • 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.

A Note on Possibilistic Correlation

  • Hong, Dug-Hun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제9권1호
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    • pp.1-3
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    • 2009
  • Recently, Carlsson, Full\acute{e}$r and Majlender [1] presented the concept of possibilitic correlation representing an average degree of interaction between marginal distribution of a joint possibility distribution as compared to their respective dispersions. They also formulated the weak and strong forms of the possibilistic Cauchy-Schwarz inequality. In this paper, we define a new probability measure. Then the weak and strong forms of the Cauchy-Schwarz inequality are immediate consequence of probabilistic Cauchy-Schwarz inequality with respect to the new probability measure.

Applications of the Schwarz Lemma and Jack's Lemma for the Holomorphic Functions

  • Ornek, Bulent Nafi;Catal, Batuhan
    • Kyungpook Mathematical Journal
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    • 제60권3호
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    • pp.507-518
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    • 2020
  • We consider a boundary version of the Schwarz Lemma on a certain class of functions which is denoted by 𝒩. For the function f(z) = z + a2z2 + a3z3 + … which is defined in the unit disc D such that the function f(z) belongs to the class 𝒩, we estimate from below the modulus of the angular derivative of the function ${\frac{f{^{\prime}^{\prime}}(z)}{f(z)}}$ at the boundary point c with f'(c) = 0. The sharpness of these inequalities is also proved.

RESULTS ASSOCIATED WITH THE SCHWARZ LEMMA ON THE BOUNDARY

  • Bulent Nafi Ornek
    • 대한수학회논문집
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    • 제38권2호
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    • pp.389-400
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    • 2023
  • In this paper, some estimations will be given for the analytic functions belonging to the class 𝓡(α). In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function h(z) and the modulus of the angular derivative of the function ${\frac{zh^{\prime}(z)}{h(z)}}$, respectively. Also, the relationship between the coefficients of the analytical function h(z) and the derivative mentioned above will be shown.

APPLICATIONS OF THE SCHWARZ LEMMA RELATED TO BOUNDARY POINTS

  • Bulent Nafi Ornek
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제30권3호
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    • pp.337-345
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    • 2023
  • Different versions of the boundary Schwarz lemma for the 𝒩 (𝜌) class are discussed in this study. Also, for the function g(z) = z+b2z2+b3z3+... defined in the unit disc D such that g ∈ 𝒩 (𝜌), we estimate a modulus of the angular derivative of g(z) function at the boundary point 1 ∈ 𝜕D with g'(1) = 1 + 𝜎 (1 - 𝜌), where ${\rho}={\frac{1}{n}}{\sum\limits_{i=1}^{n}}g(c_i)={\frac{g^{\prime}(c_1)+g^{\prime}(c_2)+{\ldots}+g^{\prime}(c_n)}{n}}{\in}g^{\prime}(D)$ and 𝜌≠1, 𝜎 > 1 and c1, c2, ..., cn ∈ 𝜕D. That is, we shall give an estimate below |g"(1)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z ≠ 0. Estimating is made by using the arithmetic average of n different derivatives g'(c1), g'(c2), ..., g'(cn).