• Title/Summary/Keyword: Fekete-Szego problem

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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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FEKETE-SZEGÖ INEQUALITIES FOR A NEW GENERAL SUBCLASS OF ANALYTIC FUNCTIONS INVOLVING THE (p, q)-DERIVATIVE OPERATOR

  • Bulut, Serap
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.723-734
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    • 2022
  • In this work, we introduce a new subclass of analytic functions of complex order involving the (p, q)-derivative operator defined in the open unit disc. For this class, several Fekete-Szegö type coefficient inequalities are derived. We obtain the results of Srivastava et al. [22] as consequences of the main theorem in this study.

COEFFICIENT ESTIMATES FOR FUNCTIONS ASSOCIATED WITH VERTICAL STRIP DOMAIN

  • Bulut, Serap
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.537-549
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    • 2022
  • In this paper, we consider a convex univalent function fα,β which maps the open unit disc 𝕌 onto the vertical strip domain Ωα,β = {w ∈ ℂ : α < ℜ < (w) < β} and introduce new subclasses of both close-to-convex and bi-close-to-convex functions with respect to an odd starlike function associated with Ωα,β. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to these classes.

APPLICATION OF GEGENBAUER POLYNOMIALS TO CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS OF ORDER ν + iς

  • Omar Alnajar;Ala Amourah;Maslina Darus
    • Korean Journal of Mathematics
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    • v.32 no.1
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    • pp.183-193
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    • 2024
  • In this paper, a new class of bi-univalent functions that are described by Gegenbauer polynomials is presented. We obtain the estimates of the Taylor-Maclaurin coefficients |m2| and |m3| for each function in this class of bi-univalent functions. In addition, the Fekete-Szegö problems function new are also studied.

FEKETE-SZEGÖ PROBLEM FOR SUBCLASSES OF STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS

  • Shanmugam, T.N.;Ramachandram, C.;Ravichandran, V.
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.589-598
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    • 2006
  • In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

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.

COEFFICIENT INEQUALITIES FOR ANALYTIC FUNCTIONS CONNECTED WITH k-FIBONACCI NUMBERS

  • Serap, Bulut;Janusz, Sokol
    • Honam Mathematical Journal
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    • v.44 no.4
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    • pp.521-534
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    • 2022
  • In this paper, we introduce a new class 𝓡kλ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σn=2 anzn (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡kλ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a3-𝜇a22| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

CERTAIN NEW FAMILIES FOR BI-UNIVALENT FUNCTIONS DEFINED BY A KNOWN OPERATOR

  • Wanas, Abbas Kareem;Choi, Junesang
    • East Asian mathematical journal
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    • v.37 no.3
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    • pp.319-331
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    • 2021
  • In this paper, we aim to introduce two new families of analytic and bi-univalent functions associated with the Attiya's operator, which is defined by the Hadamard product of a generalized Mittag-Leffler function and analytic functions on the open unit disk. Then we estimate the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we investigate Fekete-Szegö problem for these families. Some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out. Two naturally-arisen problems are given for further investigation.

Coefficient Estimates for a Subclass of Bi-univalent Functions Associated with Symmetric q-derivative Operator by Means of the Gegenbauer Polynomials

  • Amourah, Ala;Frasin, Basem Aref;Al-Hawary, Tariq
    • Kyungpook Mathematical Journal
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    • v.62 no.2
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    • pp.257-269
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    • 2022
  • In the present paper, a subclass of analytic and bi-univalent functions is defined using a symmetric q-derivative operator by means of Gegenbauer polynomials. Coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.