• Title/Summary/Keyword: Fekete-Szego inequality

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FEKETE-SZEGÖ INEQUALITY FOR A SUBCLASS OF NON-BAZILEVIĆ FUNCTIONS INVOLVING CHEBYSHEV POLYNOMIAL

  • Al-khafaji, Saba N.;Bulut, Serap;Juma, Abdul Rahman S.
    • Honam Mathematical Journal
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    • v.43 no.3
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    • pp.503-511
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    • 2021
  • In this present work, we obtain certain coefficients of the subclass 𝓗λ,𝛄(s, b, n) of non-Bazilević functions and estimate the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to this class.

COEFFICIENT INEQUALITIES FOR A UNIFIED CLASS OF BOUNDED TURNING FUNCTIONS ASSOCIATED WITH COSINE HYPERBOLIC FUNCTION

  • Gagandeep Singh;Gurcharanjit Singh;Navyodh Singh;Navjeet singh
    • The Pure and Applied Mathematics
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    • v.31 no.2
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    • pp.201-216
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    • 2024
  • The aim of this paper is to study a new and unified class 𝓡αCosh of analytic functions associated with cosine hyperbolic function in the open unit disc E = {z ∈ ℂ : |z| < 1}. Some interesting properties of this class such as initial coefficient bounds, Fekete-Szegö inequality, second Hankel determinant, Zalcman inequality and third Hankel determinant have been established. Furthermore, these results have also been studied for two-fold and three-fold symmetric functions.

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.

ESTIMATE OF THIRD ORDER HANKEL DETERMINANT FOR A CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH CARDIOID DOMAIN

  • Singh, Gagandeep;Singh, Gurcharanjit
    • The Pure and Applied Mathematics
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    • v.29 no.4
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    • pp.307-319
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    • 2022
  • The present paper deals with the upper bound of third order Hankel determinant for a certain subclass of analytic functions associated with Cardioid domain in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results proved here generalize the results of several earlier works.

On Coefficients of a Certain Subclass of Starlike and Bi-starlike Functions

  • Mahzoon, Hesam;Sokol, Janusz
    • Kyungpook Mathematical Journal
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    • v.61 no.3
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    • pp.513-522
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    • 2021
  • In this paper we investigate a subclass 𝓜(α) of the class of starlike functions in the unit disk |z| < 1. 𝓜(α), π/2 ≤ α < π, is the set of all analytic functions f in the unit disk |z| < 1 with the normalization f(0) = f'(0) - 1 = 0 that satisfy the condition $$1+\frac{{\alpha}-{\pi}}{2\;sin\;{\alpha}}. The class 𝓜(α) was introduced by Kargar et al. [Complex Anal. Oper. Theory 11: 1639-1649, 2017]. In this paper some basic geometric properties of the class 𝓜(α) are investigated. Among others things, coefficients estimates and bound are given for the Fekete-Szegö functional associated with the k-th root transform [f(zk)]1/k. Also a certain subclass of bi-starlike functions is introduced and the bounds for the initial coefficients are obtained.

MULTIVALENT NON-CARATHÉODORY FUNCTIONS INVOLVING HIGHER ORDER DERIVATIVES

  • Daniel Breaz;Kadhavoor Ragavan Karthikeyan;Sakkarai Lakshmi;Alagiriswamy Senguttuvan
    • Communications of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.657-671
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    • 2024
  • In this paper, we use higher order derivatives with regard to symmetric points to introduce a class of multivalent starlike functions. The major deviation is that we define some differential characterizations that are subordinate to a function whose real part is not greater than zero. The primary outcomes of this study are initial coefficients and the Fekete-Szegő inequality for functions falling under the given class. Also, we have obtained an interesting subordination results involving symmetric functions. The results obtained here extend or unify the various other well-known and new results.