• Title, Summary, Keyword: univalent function

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COEFFICIENTS OF UNIVALENT HARMONIC MAPPINGS

  • Jun, Sook Heui
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.349-353
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    • 2007
  • In this paper, we obtain some coefficient bounds of harmonic univalent mappings by using properties of the analytic univalent function on ${\Delta}$={z : |z| > 1}.

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CONSTANTS FOR HARMONIC MAPPINGS

  • Jun, Sook Heui
    • Journal of the Chungcheong Mathematical Society
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    • v.17 no.2
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    • pp.163-167
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    • 2004
  • In this paper, we obtain some coefficient estimates of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}$ = {z : |z| > 1}.

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UNIFORMLY LOCALLY UNIVALENT FUNCTIONS

  • Song, Tai-Sung
    • The Pure and Applied Mathematics
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    • v.6 no.2
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    • pp.87-93
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    • 1999
  • A holomorphic function f on D = {z : │z│ < 1} is called uniformly locally univalent if there exists a positive constant $\rho$ such that f is univalent in every hyperbolic disk of hyperbolic radius $\rho$. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.

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UNIVALENT HARMONIC EXTERIOR MAPPINGS

  • Jun, Sook Heui
    • Journal of the Chungcheong Mathematical Society
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    • v.16 no.2
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    • pp.31-41
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    • 2003
  • In this paper, we will show that the bounds for coefficients of harmonic, orientation-preserving, univalent mappings f defined on ${\Delta}$ = {z : |z| > 1} with $f({\Delta})={\Delta}$ are sharp by finding extremal functions.

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Partial Sums of Starlike Harmonic Univalent Functions

  • Porwal, Saurabh;Dixit, Kaushal Kishore
    • Kyungpook Mathematical Journal
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    • v.50 no.3
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    • pp.433-445
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    • 2010
  • Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.

BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER BASED ON SUBORDINATE CONDITIONS INVOLVING HURWITZ-LERCH ZETA FUNCTION

  • Murugusundaramoorthy, G.;Janani, T.;Cho, Nak Eun
    • East Asian mathematical journal
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    • v.32 no.1
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    • pp.47-59
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    • 2016
  • The purpose of the present paper is to introduce and investigate two new subclasses of bi-univalent functions of complex order defined in the open unit disk, which are associated with Hurwitz-Lerch zeta function and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$ for functions in the new subclasses. Several (known or new) consequences of the results are also pointed out.

COEFFICIENT BOUNDS FOR INVERSE OF FUNCTIONS CONVEX IN ONE DIRECTION

  • Maharana, Sudhananda;Prajapat, Jugal Kishore;Bansal, Deepak
    • Honam Mathematical Journal
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    • v.42 no.4
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    • pp.781-794
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    • 2020
  • In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szegö functional and third order Hankel determinant for these classes have also investigated.

SOME RESULTS ASSOCIATED WITH CERTAIN ANALYTIC AND UNIVALENT FUNCTIONS INVOLVING FRACTIONAL DERIVATIVE OPERATORS

  • Irmak, H.;Raina, R.K.
    • East Asian mathematical journal
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    • v.21 no.2
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    • pp.219-231
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    • 2005
  • This paper investigates some results (Theorems 2.1-2.3, below) concerning certain classes of analytic and univalent functions, involving the familiar fractional derivative operators. We state interesting consequences arising from the main results by mentioning the cases connected with the starlikeness, convexity, close-to-convexity and quasi-convexity of geometric function theory. Relevant connections with known results are also emphasized briefly.

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SOME MORE COUNTEREXAMPLES FOR BOMBIERI'S CONJECTURE ON UNIVALENT FUNCTIONS

  • Efraimidis, Iason;Pastor, Carlos
    • Journal of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1485-1498
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    • 2018
  • We disprove a conjecture of Bombieri regarding univalent functions in the unit disk in some previously unknown cases. The key step in the argument is showing that the global minimum of the real function (n sin x - sin(nx))/(m sin x - sin(mx)) is attained at x = 0 for integers m > $n{\geq}2$ when m is odd and n is even, m is sufficiently big and $0.5{\leq}n/m{\leq}0.8194$.

ON A CLASS OF q-BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER RELATED TO SHELL-LIKE CURVES CONNECTED WITH THE FIBONACCI NUMBERS

  • Ahuja, Om P.;Cetinkaya, Asena;Bohra, Nisha
    • Honam Mathematical Journal
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    • v.42 no.2
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    • pp.319-330
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    • 2020
  • We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.