• Title/Summary/Keyword: starlike functions of complex order

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SOME MAJORIZATION PROBLEMS ASSOCIATED WITH p-VALENTLY STARLIKE AND CONVEX FUNCTIONS OF COMPLEX ORDER

  • Altintas, Osman;Srivastava, H.M.
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.175-183
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    • 2001
  • The main object of this paper is to investigate several majorization problems involving two subclasses $S_{p,q}(\gamma)$ and $C_{p,q}(\gamma)$ of p-valently starlike and p-valently convex functions of complex order ${\gamma}{\neq}0$ in the open unit disk $\mathbb{u}$. Relevant connections of the results presented here with those given by earlier workers on the subject are also indicated.

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MAJORIZATION PROBLEMS FOR UNIFORMLY STARLIKE FUNCTIONS BASED ON RUSCHEWEYH q-DIFFERENTIAL OPERATOR RELATED WITH EXPONENTIAL FUNCTION

  • Vijaya, K.;Murugusundaramoorthy, G.;Cho, N.E.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.1
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    • pp.71-81
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    • 2021
  • The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

Certain Subclasses of Bi-Starlike and Bi-Convex Functions of Complex Order

  • MAGESH, NANJUNDAN;BALAJI, VITTALRAO KUPPARAOo
    • Kyungpook Mathematical Journal
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    • v.55 no.3
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    • pp.705-714
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    • 2015
  • In this paper, we introduce and investigate an interesting subclass $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ of analytic and bi-univalent functions of complex order in the open unit disk ${\mathbb{U}}$. For functions belonging to the class $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ we investigate the coefficient estimates on the first two Taylor-Maclaurin coefficients ${\mid}{\alpha}_2{\mid}$ and ${\mid}{\alpha}_3{\mid}$. The results presented in this paper would generalize and improve some recent works of [1],[5],[9].

SUFFICIENT CONDITIONS FOR UNIVALENCE OF A GENERAL INTEGRAL OPERATOR

  • Selvaraj, Chellian;Karthikeyan, Kadhavoor Ragavan
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.367-372
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    • 2009
  • In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.

On the Fekete-Szegö Problem for Starlike Functions of Complex Order

  • Darwish, Hanan;Lashin, Abdel-Moniem;Al Saeedi, Bashar
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.477-484
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    • 2020
  • For a non-zero complex number b and for m and n in 𝒩0 = {0, 1, 2, …} let Ψn,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dn f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a3 - 𝜇a22| are obtained.

ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF GENERAL SUBCLASSES OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER INVOLVING SUBORDINATION

  • Altinkaya, Sahsene;Yalcin, Sibel
    • Honam Mathematical Journal
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    • v.40 no.3
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    • pp.391-400
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    • 2018
  • The object of this paper to construct a new class $$A^m_{{\mu},{\lambda},{\delta}}({\alpha},{\beta},{\gamma},t,{\Psi})$$ of bi-univalent functions of complex order defined in the open unit disc. The second and the third coefficients of the Taylor-Maclaurin series for functions in the new subclass are determined. Several special consequences of the results are also indicated.

ON PROPERTIES OF COMPLEX ORDER FOR THE CLASSES OF UNIVALENT FUNCTIONS

  • Park, Suk-Joo
    • The Pure and Applied Mathematics
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    • v.2 no.2
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    • pp.115-126
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    • 1995
  • Let A be the class of univalent functions f(z)=z+${\alpha}$$_2$z$^2$${\alpha}$$_3$z$^3$+…(1.1) which are analytic in the unit disk $\Delta$= {z:│z│<1}. Let S*(p) be the subclass of A composing of functions which are starlike of order $\rho$. A function f(z) belonging to the class A is said to be starlike of order $\rho$ ($\rho$(equation omitted) 0) if and only if z$\^$-l/ f(z) (equation omitted) 0 (z$\in$$\Delta$) and (equation omitted (1.2).(omitted)

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