The logarithmic coefficients gamma(n) of an analytic and univalent function f in the unit disc D = {z is an element of C : vertical bar z vertical bar < 1} with the normalisation f (0) = 0 = f'(0) - 1 are defin...
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The logarithmic coefficients gamma(n) of an analytic and univalent function f in the unit disc D = {z is an element of C : vertical bar z vertical bar < 1} with the normalisation f (0) = 0 = f'(0) - 1 are defined by log(f (z)/z) = 2 Sigma(infinity)(n=1)gamma(n)z(n). In the present paper, we consider close-to-convex functions (with argument 0) with respect to odd starlike functions and determine the sharp upper bound of vertical bar gamma(n)vertical bar, n = 1;2;3, for such functions f.
The analytic functions, mapping the open unit disk onto petal and oval type regions, introduced by Noor and Malik (Comput. Math. Appl. 62:2209-2217, 2011), are considered to define and study their associated close-to-...
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The analytic functions, mapping the open unit disk onto petal and oval type regions, introduced by Noor and Malik (Comput. Math. Appl. 62:2209-2217, 2011), are considered to define and study their associated close-to-convex functions. This work includes certain geometric properties like sufficiency criteria, coefficient estimates, arc length, the growth rate of coefficients of Taylor series, integral preserving properties of these functions.
Given α∈[0, 1], let hα（z） ：= z/（1 - αz）, z ∈ D ：= {z ∈ C： ｜z｜ 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ （-π/2, π/2）...
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Given α∈[0, 1], let hα（z） ：= z/（1 - αz）, z ∈ D ：= {z ∈ C： ｜z｜ 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ （-π/2, π/2） such that Re{e^iδ zf′（z）/hα（z）} 〉 0, z ∈ D. For the class l（hα） of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied.
Given a starlike function g is an element of S*, an analytic standardly normalized function f in the unit disk D is called close-to-convex with respect to g if there exists delta is an element of (-pi/2, pi/2) such th...
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Given a starlike function g is an element of S*, an analytic standardly normalized function f in the unit disk D is called close-to-convex with respect to g if there exists delta is an element of (-pi/2, pi/2) such that Re{e(i delta)zf'(z)/g(z)} > 0, z is an element of D. For the class C(h) of all close-to-convex functions with respect to h(z) := z/(1 - z), z is an element of D, a Fekete-Szego problem is examined.
Let be the elliptical domain Let denote the class of functions F analytic and univalent in satisfying the normalization conditions and In this paper, we obtain sharp bounds for the Faber coefficients of functions whic...
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Let be the elliptical domain Let denote the class of functions F analytic and univalent in satisfying the normalization conditions and In this paper, we obtain sharp bounds for the Faber coefficients of functions which belong to certain subclasses of
An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,...
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An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functionsconvex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
Given alpha epsilon [0, 1], let g(alpha)(z) := z/(1 - alpha z)(2), z epsilon D := {z epsilon C : vertical bar z vertical bar 0, z epsilon D. For the class C(g(alpha)) of all close-to-convex functions with respect to ...
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Given alpha epsilon [0, 1], let g(alpha)(z) := z/(1 - alpha z)(2), z epsilon D := {z epsilon C : vertical bar z vertical bar < 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to g(alpha) if there exists delta epsilon (-pi/2,pi/2) such that Re {e(i delta)zf'(z)/g(alpha)(z)} > 0, z epsilon D. For the class C(g(alpha)) of all close-to-convex functions with respect to g(alpha), the Fekete-Szego problem is studied.
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.
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.
In the present paper, we introduce and investigate a certain new subclass MKs (lambda,A,B) of meromorphic close-to-convex functions. Such results as inclusion relationships, coefficient inequalities and convolution pr...
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In the present paper, we introduce and investigate a certain new subclass MKs (lambda,A,B) of meromorphic close-to-convex functions. Such results as inclusion relationships, coefficient inequalities and convolution property are derived. Relevant connections of the results presented here with those obtained in earlier works are also pointed out. (C) 2013 Elsevier Inc. All rights reserved.
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