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

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CERTAIN PROPERTIES OF A NEW SUBCLASS OF ANALYTIC AND p-VALENTLY CLOSE-TO-CONVEX FUNCTIONS

  • BULUT, Serap
    • Honam Mathematical Journal
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    • v.39 no.2
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    • pp.233-245
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    • 2017
  • In the present paper we introduce and investigate an interesting subclass ${\mathcal{K}}^{(k)}_s({\gamma},p) $ of analytic and p-valently close-to-convex functions in the open unit disk ${\mathbb{U}}$. For functions belonging to this class, we derive several properties as the inclusion relationships and distortion theorems. The various results presented here would generalize many known recent results.

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

  • Bulut, Serap
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.789-797
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    • 2020
  • By considering a certain univalent function in the open unit disk ��, that maps �� onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential equation. We determine the coefficient bounds for functions in this new class. Relevant connections of some of the results obtained with those in earlier works are also provided.

GENERALIZED CLOSE-TO-CONVEX FUNCTIONS

  • NOOR, KHALIDA INAYAT
    • Honam Mathematical Journal
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    • v.17 no.1
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    • pp.97-106
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    • 1995
  • We introduce a new class of analytic functions in the unit disk which generalizes the concepts of close-to-convexity and of bounded boundary rotation, and study its various properties including its connection with other classes of analytic and univalent functions.

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ON THE $FEKETE-SZEG\"{O}$ PROBLEM FOR STRONGLY $\alpha$-LOGARITHMIC CLOSE-TO-CONVEX FUNCTIONS

  • Cho, Nak-Eun
    • East Asian mathematical journal
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    • v.21 no.2
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    • pp.233-240
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    • 2005
  • Let $CS^{\alpha}(\beta)$ denote the class of normalized strongly $\alpha$-logarithmic close-to-convex functions of order $\beta$, defined in the open unit disk $\mathbb{U}$ by $$\|arg\{\(\frac{f(z)}{g(z)}\)^{1-\alpha}\(\frac{zf'(z)}{g(z)\)^{\alpha}\}\|\leq\frac{\pi}{2}\beta,\;(\alpha,\beta\geq0)$$ where $g{\in}S^*$ the class of normalized starlike functions. In this paper, we prove sharp $Fekete-Szeg\"{o}$ inequalities for functions $f{\in}CS^{\alpha}(\beta)$.

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