• Title, Summary, Keyword: bi-univalent functions

Search Result 18, Processing Time 0.029 seconds

UPPER BOUND OF SECOND HANKEL DETERMINANT FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER

  • Mustafa, Nizami
    • Communications of the Korean Mathematical Society
    • /
    • v.34 no.3
    • /
    • pp.783-797
    • /
    • 2019
  • In this paper, we introduce and investigate a subclass ${\Im}_{\Sigma}({\alpha},{\beta},{\gamma})$ of analytic and bi-univalent functions of complex order in the open unit disk U in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

FEKETE-SZEGÖ INEQUALITIES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR

  • BULUT, Serap
    • Honam Mathematical Journal
    • /
    • v.39 no.4
    • /
    • pp.591-601
    • /
    • 2017
  • In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.

COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

  • Panigrahi, Trailokya
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.5
    • /
    • pp.1531-1538
    • /
    • 2013
  • In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions $w=f(z)$ defined on $\tilde{\Delta}:=\{z{\in}\mathbb{C}:1<{\mid}z{\mid}<{\infty}\}$ whose inverse $f^{-1}(w)$ is also univalent meromorphic in $\tilde{\Delta}$. Estimates for the initial coefficients are obtained for the functions in these new subclasses.

COEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS

  • Adegani, Ebrahim Analouei;Bulut, Serap;Zireh, Ahmad
    • Bulletin of the Korean Mathematical Society
    • /
    • v.55 no.2
    • /
    • pp.405-413
    • /
    • 2018
  • In this work, we use the Faber polynomial expansions to find upper bounds for the coefficients of analytic bi-univalent functions in subclass $\Sigma({\tau},{\gamma},{\varphi})$ which is defined by subordination conditions in the open unit disk ${\mathbb{U}}$. In certain cases, our estimates improve some of those existing coefficient bounds.

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
    • /
    • v.32 no.1
    • /
    • pp.47-59
    • /
    • 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 ESTIMATES FOR CERTAIN SUBCLASS OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

  • Salehian, Safa;Zireh, Ahmad
    • Communications of the Korean Mathematical Society
    • /
    • v.32 no.2
    • /
    • pp.389-397
    • /
    • 2017
  • In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on ${\Delta}=\{z{\in}{\mathbb{C}}$ : 1 < |z| < ${\infty}\}$. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.

Coefficient Bounds for Bi-spirallike Analytic Functions

  • Soren, Madan Mohan;Mishra, Akshaya Kumar
    • Kyungpook Mathematical Journal
    • /
    • v.58 no.4
    • /
    • pp.697-709
    • /
    • 2018
  • In the present paper, we introduce and investigate two new subclasses, namely; the class of strongly ${\alpha}$-bi-spirallike functions of order ${\beta}$ and ${\alpha}$-bi-spirallike functions of order ${\rho}$, of the function class ${\Sigma};$ of normalized analytic and bi-univalent functions in the open unit disk $$U=\{z:z{\in}C\;and\;{\mid}z{\mid}<1\}$$. We find estimates on the coefficients ${\mid}a_2{\mid}$, ${\mid}a_3{\mid}$ and ${\mid}a_4{\mid}$ for functions in these two subclasses.

THE FEKETE-SZEGÖ COEFFICIENT INEQUALITY FOR A NEW CLASS OF m-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS SATISFYING SUBORDINATION CONDITION

  • Akgul, Arzu
    • Honam Mathematical Journal
    • /
    • v.40 no.4
    • /
    • pp.733-748
    • /
    • 2018
  • In this paper, we investigate a new subclass $S^{{\varphi},{\lambda}}_{{\Sigma}_m}$ of ${\Sigma}_m$ consisting of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-$Szeg{\ddot{o}}$ inequalities for this class. Also, we establish estimates for the coefficients for this subclass and several related classes are also considered and connections to earlier known results are made.

NEW SUBCLASS OF BI-UNIVALENT FUNCTIONS BY (p, q)-DERIVATIVE OPERATOR

  • Motamednezhad, Ahmad;Salehian, Safa
    • Honam Mathematical Journal
    • /
    • v.41 no.2
    • /
    • pp.381-390
    • /
    • 2019
  • In this paper, we introduce interesting subclasses ${\mathcal{H}}^{p,q,{\beta},{\alpha}}_{{\sigma}B}$ and ${\mathcal{H}}^{p,q,{\beta}}_{{\sigma}B}({\gamma})$ of bi-univalent functions by (p, q)-derivative operator. Furthermore, we find upper bounds for the second and third coefficients for functions in these subclasses. The results presented in this paper would generalize and improve some recent works of several earlier authors.