In the present paper, we introduce a new subclass of the class of close-to-convex functions. The subordination and inclusion relationship, and some coefficient inequalities, a sufficient condition for this class are p...
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In the present paper, we introduce a new subclass of the class of close-to-convex functions. The subordination and inclusion relationship, and some coefficient inequalities, a sufficient condition for this class are provided. Furthermore, we obtain the distortion theorems. The results presented here would provide extensions of those given in earlier works. (C) 2011 Elsevier Inc. All rights reserved.
In the present paper certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szeg functional for functions belonging to our class, coefficient estimates an...
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In the present paper certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szeg functional for functions belonging to our class, coefficient estimates and a sufficient condition. The results presented here would provide extensions of those given in some earlier works.
We derive general formula for the fourth coefficient of the functions belonging to the Carath & eacute;odory class involving the parameters lying in the open unit disk. Further, we obtain sharp upper bounds of ini...
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We derive general formula for the fourth coefficient of the functions belonging to the Carath & eacute;odory class involving the parameters lying in the open unit disk. Further, we obtain sharp upper bounds of initial inverse coefficients for certain close-to-convex functions satisfying any one of the inequalities: Re((1 - z)f ' (z)) >0, Re((1 - z(2))f ' (z)) > 0, Re((1 - z + z(2))f '(z)) > 0 and Re((1-z)(2 )f ' (z)) > 0.
For ß Oy Kß denotes the set of functions {formula present /(z) = z + ü2Z + • • • defined on the unit disc U with the representation f'{z) =* ap^{z)s{z)/zy where a S C, p is an analytic function with...
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LetC1(β) be the class of normalized functionsfwhich are analytic in the open unit disku, given by the power series:and satisfy the inequality:for some normalized univalent and convex function φ. In this paper we sol...
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LetC1(β) be the class of normalized functionsfwhich are analytic in the open unit disku, given by the power series:and satisfy the inequality:for some normalized univalent and convex function φ. In this paper we solve the Fekete-Szego problem for the family:by proving that
Abstract: In this paper we introduce new subclasses of the class of close-to-convex functions. We call a regular function $f(z)$ an alpha-close-to-convex function if $(f(z)f’(z)/z) \ne 0$ for z in E and if fo...
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Abstract: In this paper we introduce new subclasses of the class of close-to-convex functions. We call a regular function $f(z)$ an alpha-close-to-convex function if $(f(z)f’(z)/z) \ne 0$ for z in E and if for some nonnegative real number $\alpha$ there exists a starlike function $\phi (z) = z + \cdots$ such that \[ \operatorname {Re} \;\left [ {(1 - \alpha )\frac {{zf’(z)}}{{\phi (z)}} + \alpha \frac {{(zf’(z))’}}{{\phi ’(z)}}} \right ] > 0\] for z in E. We have proved that all alpha-close-to-convex functions are close-to-convex and have obtained a few coefficient inequalities for $\alpha$-close-to-convex functions and an integral formula for constructing these functions. Let ${\mathfrak {F}_\alpha }$ be the class of regular and normalised functions $f(z)$ which satisfy $\operatorname {Re} \;(f’(z) + \alpha zf''(z)) > 0$ for z in E. $f(z) \in {\mathfrak {F}_\alpha }$ gives $\operatorname {Re} f’(z) > 0$ for z in E provided $\operatorname {Re} \alpha \geqslant 0$. A sharp radius of univalence of the class of functions $f(z)$ for which $zf’(z) \in {\mathfrak {F}_\alpha }$ has also been obtained.
The object of this article is to prove the uniqueness of the composition ƒ − ρ ∞ φ, where ρ is a polynomial of degree at most ρ and φ is a normalized univalent function, whenever ƒ is a close-to-convex function ...
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The object of this article is to prove the uniqueness of the composition ƒ − ρ ∞ φ, where ρ is a polynomial of degree at most ρ and φ is a normalized univalent function, whenever ƒ is a close-to-convex function of order ρ. We also give an example of a weakly close-to-convex function ƒ = ρ∞φ with four critical points, and for which ρ is a polynomial of degree five, φ is a normalized univalent function, but the composition is not unique.
In this paper, we investigate the upper bound associated with the second Hankel determinant H-2(2) for a certain class of bi-close-to-convex functions which we have introduced here. Several closely related results are...
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In this paper, we investigate the upper bound associated with the second Hankel determinant H-2(2) for a certain class of bi-close-to-convex functions which we have introduced here. Several closely related results are also considered.
In this paper, we consider a new class C(phi,psi,eta) of analytic functions defined by means of subordination. Coefficient bounds, Fekete-Szego problem and norm estimates of the pre-Schwarzian derivatives of functions...
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In this paper, we consider a new class C(phi,psi,eta) of analytic functions defined by means of subordination. Coefficient bounds, Fekete-Szego problem and norm estimates of the pre-Schwarzian derivatives of functions belonging to the class C(phi,psi,eta) are investigated. A class of multiple close-to-convex functions is also considered.
Abstract: It is the object of this article to define close-to-convex multivalent functions in terms of weakly starlike multivalent functions. Six classes are defined, and shown to be equal. These generalize th...
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Abstract: It is the object of this article to define close-to-convex multivalent functions in terms of weakly starlike multivalent functions. Six classes are defined, and shown to be equal. These generalize the class of close-to-convex functions developed by Livingston in the article, $p$-valent close-to-convex functions, Trans. Amer. Math. Soc. 115 (1965), 161-179.
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