• Title/Summary/Keyword: close-to-convex functions

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GEOMETRIC PROPERTIES OF GENERALIZED DINI FUNCTIONS

  • Deniz, Erhan;Goren, Seyma
    • Honam Mathematical Journal
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    • v.41 no.1
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    • pp.101-116
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    • 2019
  • In this paper our aim is to establish some geometric properties (like starlikeness, convexity and close-to-convexity) for the generalized and normalized Dini functions. In order to prove our main results, we use some inequalities for ratio of these functions in normalized form and classical result of Fejer.

On a Class of Analytic Functions Related to the Starlike Functions

  • Gao, Chunyi;Zhou, Shiqiong
    • Kyungpook Mathematical Journal
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    • v.45 no.1
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    • pp.123-130
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    • 2005
  • In this paper we discuss a class of analytic functions related to the starlike functions in the unit disk. We prove that this class belongs to the class of close-to-convex functions, we obtain the sharp coefficient upper bounds and distortion theorem of this class, we also get the convexity radius of this class.

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SEVERAL PROPERTIES OF THE SUBCLASS OF Gk DESCRIBED BY SUBORDINATION

  • PARK, YOUNG OK
    • Honam Mathematical Journal
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    • v.21 no.1
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    • pp.139-147
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    • 1999
  • In this paper we generalize the definition of strongly close-to-convex functions by using the functions g(z) of bounded boundary rotation and investigate the distortion and rotation theorem, coefficient inequalities, invariance property and inclusion relation for the new class $G_{k}[A,\;B]$.

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A CERTAIN SUBCLASS OF JANOWSKI TYPE FUNCTIONS ASSOCIATED WITH κ-SYMMETRIC POINTS

  • Kwon, Ohsang;Sim, Youngjae
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.143-154
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    • 2013
  • We introduce a subclass $S_s^{({\kappa})}$(A,B) (-1 ${\leq}$ B < A ${\leq}$ 1) of functions which are analytic in the open unit disk and close-to-convex with respect to ${\kappa}$-symmetric points. We give some coefficient inequalities, integral representations and invariance properties of functions belonging to this class.

COEFFICIENT BOUNDS FOR p-VALENTLY CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH VERTICAL STRIP DOMAIN

  • Bulut, Serap
    • Korean Journal of Mathematics
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    • v.29 no.2
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    • pp.395-407
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    • 2021
  • By considering a certain univalent function that maps the unit disk 𝕌 onto a strip domain, we introduce new subclasses of analytic and p-valent functions and determine the coefficient bounds for functions belonging to these new classes. Relevant connections of some of the results obtained with those in earlier works are also provided.

ON THE FEKETE-SZEGO PROBLEM FOR CERTAIN ANALYTIC FUNCTIONS

  • Kwon, Oh-Sang;Cho, Nak-Eun
    • The Pure and Applied Mathematics
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    • v.10 no.4
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    • pp.265-271
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    • 2003
  • Let $CS_\alpha(\beta)$ denote the class of normalized strongly $\alpha$-close-to-convex functions of order $\beta$, defined in the open unit disk $\cal{U}$ of $\mathbb{C}$${\mid}arg{(1-{\alpha})\frac{f(z)}{g(z)}+{\alpha}\frac{zf'(z)}{g(z)}}{\mid}\;\leq\frac{\pi}{2}{\beta}(\alpha,\beta\geq0)$ such that $g\; \in\;S^{\ask}$, the class of normalized starlike unctions. In this paper, we obtain the sharp Fekete-Szego inequalities for functions belonging to $CS_\alpha(\beta)$.

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ON UNIVALENT SUBORDINATE FUNCTIONS

  • Park, Suk-Joo
    • The Pure and Applied Mathematics
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    • v.3 no.2
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    • pp.103-111
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    • 1996
  • Let $f(z)=z+\alpha_2 z^2$+…+ \alpha_{n}z^n$+… be regular and univalent in $\Delta$ = {z : │z│<1}. In this paper, using the proper subordinate functions, we investigate the some relations between subordinations and conditions of functions belonging to subclasses of univalent functions.

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SOME CRITERIA FOR p-VALENT FUNCTIONS

  • Yang, Dinggong
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.571-582
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    • 1998
  • The object of the present paper is to derive some sufficient conditions for p-valently close-to-convexity, p-valently starlikeness and p-valently convexity.

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HIGHER ORDER CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH RUSCHEWEYH DERIVATIVE OPERATOR

  • NOOR, KHALIDA INAYAT;SHAH, SHUJAAT ALI
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.133-143
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    • 2021
  • The purpose of this paper is to introduce and study certain subclasses of analytic functions by using Ruscheweyh derivative operator. We discuss various of interesting properties such as, necessary condition, arc length problem and growth rate of coefficient of newly defined class. Also rate of growth of Hankel determinant will be estimated.