On the maximum of $a_4 - 3a_2 a_3 + μa_2$ and some related functionals for bounded real univalent functions

Z. J. Jakubowski; H. Siejka; O. Tammi

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Displaying similar documents to “On the maximum of $a_{4} - 3 a_{2} a_{3} + μ a_{2}$ and some related functionals for bounded real univalent functions”

Sharp estimation of the coefficients of bounded univalent functions close to identity

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CONTENTSIntroduction...............................................................................................................................................................................5Definitions and notation.........................................................................................................................................................7The main result........................................................................................................................................................................91....

Estimates of the real part of $\frac{f (z)}{z}$ for some classes of univalent functions

M. Obradović (1984)

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Region of variability for functions with positive real part

Saminathan Ponnusamy, Allu Vasudevarao (2010)

Annales Polonici Mathematici

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For γ ∈ ℂ such that |γ| < π/2 and 0 ≤ β < 1, let $_{γ, β}$ denote the class of all analytic functions P in the unit disk with P(0) = 1 and $R e (e^{i γ} P (z)) > β c o s γ$ in . For any fixed z₀ ∈ and λ ∈ ̅, we shall determine the region of variability $V_{} (z ₀, λ)$ for $\int_{0}^{z ₀} P (ζ) d ζ$ when P ranges over the class $(λ) = P \in_{γ, β} : P^{'} (0) = 2 (1 - β) λ e^{- i γ} c o s γ .$ As a consequence, we present the region of variability for some subclasses of univalent functions. We also graphically illustrate the region of variability for several sets of parameters.

Some properties for $α$ -starlike functions with respect to $k$ -symmetric points of complex order

H. E. Darwish, A. Y. Lashin, S. M. Sowileh (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In the present work, we introduce the subclass $𝒯_{γ, α}^{k} (ϕ)$ , of starlike functions with respect to $k$ -symmetric points of complex order $γ$ ( $γ \neq 0$ ) in the open unit disc . Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.

A Short Proof of the Variational Principle for a $ℤ_{+}^{N}$ Action on a Compact Space

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Generalized problem of starlikeness for products of close-to-star functions

Jacek Dziok (2013)

Annales Polonici Mathematici

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We consider functions of the type $F (z) = z \prod_{j = 1}^{n} {[f_{j} (z) / z]}^{a_{j}}$ , where $a_{j}$ are real numbers and $f_{j}$ are $β_{j}$ -strongly close-to-starlike functions of order $α_{j}$ . We look for conditions on the center and radius of the disk (a,r) = z:|z-a| < r, |a| < r ≤ 1 - |a|, ensuring that F((a,r)) is a domain starlike with respect to the origin.

An integral operator on the classes $𝒮^{*} (α)$ and $𝒞𝒱ℋ (β)$

Nicoleta Ularu, Nicoleta Breaz (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order $α$ and from the class $𝒞𝒱ℋ (β)$ and also we estimate the first two coefficients for functions obtained by this operator applied on the class $𝒞𝒱ℋ (β)$ .

Convolution conditions for bounded $α$ -starlike functions of complex order

A. Y. Lashin (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let $A$ be the class of analytic functions in the unit disc $U$ of the complex plane $ℂ$ with the normalization $f (0) = f^{^{'}} (0) - 1 = 0$ . We introduce a subclass $S_{M}^{*} (α, b)$ of $A$ , which unifies the classes of bounded starlike and convex functions of complex order. Making use of Salagean operator, a more general class $S_{M}^{*} (n, α, b)$ ( $n \geq 0$ ) related to $S_{M}^{*} (α, b)$ is also considered under the same conditions. Among other things, we find convolution conditions for a function $f \in A$ to belong to the class $S_{M}^{*} (α, b)$ . Several properties of the class $S_{M}^{*} (n, α, b)$ are investigated. ...

A penalty approach for a box constrained variational inequality problem

Zahira Kebaili, Djamel Benterki (2018)

Applications of Mathematics

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We propose a penalty approach for a box constrained variational inequality problem $(BVIP)$ . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of $BVIP$ when the function $F$ involved is continuous and strongly monotone and the box $C$ contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results...

A note on the functions $(S_{n} f) (z)$ defined by Ruscheweyn

S. Owa, C. Y. Shen (1988)

Matematički Vesnik

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Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

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We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function $f : W \to X$ defined on a non-degenerate closed subinterval $W$ of $ℝ^{m}$ in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure $V_{ℳ} F$ generated by the primitive $F : ℐ_{W} \to X$ of $f$ , where $ℐ_{W}$ is the family of all closed non-degenerate subintervals of $W$ .

Properties of functions concerned with Caratheodory functions

Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let $𝒫_{n}$ denote the class of analytic functions $p (z)$ of the form $p (z) = 1 + c_{n} z^{n} + c_{n + 1} z^{n + 1} + \dots$ in the open unit disc $𝕌$ . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for $p (z)$ concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

Sakaguchi type functions defined by balancing polynomials

Gunasekar Saravanan, Sudharsanan Baskaran, Balasubramaniam Vanithakumari, Serap Bulut (2025)

Mathematica Bohemica

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The class of Sakaguchi type functions defined by balancing polynomials has been introduced as a novel subclass of bi-univalent functions. The bounds for the Fekete-Szegö inequality and the initial coefficients $| a_{2} |$ and $| a_{3} |$ have also been estimated.

Injectivity of sections of convex harmonic mappings and convolution theorems

Liulan Li, Saminathan Ponnusamy (2016)

Czechoslovak Mathematical Journal

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We consider the class $ℋ_{0}$ of sense-preserving harmonic functions $f = h + \bar{g}$ defined in the unit disk $| z | < 1$ and normalized so that $h (0) = 0 = h^{'} (0) - 1$ and $g (0) = 0 = g^{'} (0)$ , where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $𝒫_{H}^{0} (α)$ and $𝒢_{H}^{0} (β)$ of functions from $ℋ_{0}$ and show that if $f \in 𝒫_{H}^{0} (α)$ and $F \in 𝒢_{H}^{0} (β)$ , then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters $α$ and $β$ are satisfied. In the second part we study the harmonic sections...

On certain general integral operators of analytic functions

B. A. Frasin (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper, we obtain new sufficient conditions for the operators $F_{α_{1}, α_{2}, . . ., α_{n}, β} (z)$ and $G_{α_{1}, α_{2}, . . ., α_{n}, β} (z)$ to be univalent in the open unit disc $𝒰$ , where the functions $f_{1}, f_{2}, . . ., f_{n}$ belong to the classes $S^{*} (a, b)$ and $𝒦 (a, b)$ . The order of convexity for the operators $F_{α_{1}, α_{2}, . . ., α_{n}, β} (z)$ and $G_{α_{1}, α_{2}, . . ., α_{n}, β} (z)$ is also determined. Furthermore, and for $β = 1$ , we obtain sufficient conditions for the operators $F_{n} (z)$ and $G_{n} (z)$ to be in the class $𝒦 (a, b)$ . Several corollaries and consequences of the main results are also considered.

Finite element variational crimes in the case of semiregular elements

Alexander Ženíšek (1996)

Applications of Mathematics

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The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain $Ω$ whose boundary $\partial Ω$ is formed by two circles $Γ_{1}$ , $Γ_{2}$ with the same center $S_{0}$ and radii $R_{1}$ , $R_{2} = R_{1} + ϱ$ , where $ϱ ≪ R_{1}$ . On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for $u = 0$ are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus...

A characterization of the disc $D^{n}$

Th. Friedrich (1974)

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On spirallike functions of order $α$ and type $β$ with fixed second coefficient

M. K. Aouf (1988)

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Pressure and recurrence

Véronique Maume-Deschamps, Bernard Schmitt, Mariusz Urbański, Anna Zdunik (2003)

Fundamenta Mathematicae

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We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) $l i m_{n \to \infty} n^{- 1} l o g \sum_{j = 0}^{τ ₙ (x)} μ (α ⁿ (T^{j} (x)))$ , where $α ⁿ (T^{j} (x))$ is the element of the partition containing $T^{j} (x)$ and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).

Displaying similar documents to “On the maximum of a 4 - 3 a 2 a 3 + μ a 2 and some related functionals for bounded real univalent functions”

Displaying similar documents to “On the maximum of $a_{4} - 3 a_{2} a_{3} + μ a_{2}$ and some related functionals for bounded real univalent functions”