For analytic functions f in the unit disk D normalized by f(0)=0 and f ' (0)=1 satisfying in D respectively the conditions {(1-z)f ' (z)}>0,mml:mspace width="0.166667em"mml:mspace>{(1-z2)f '...
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For analytic functions f in the unit disk D normalized by f(0)=0 and f ' (0)=1 satisfying in D respectively the conditions {(1-z)f ' (z)}>0,mml:mspace width="0.166667em"mml:mspace>{(1-z2)f ' (z)}>0,mml:mspace width="4pt"mml:mspace mml:mspace width="0.166667em"/mml:mspace>ReRe mml:mspace width="0.166667em"mml:mspace>{(1-z)2f ' (z)}>0, the sharp upper bound of the third logarithmic coefficient in case when f ' ' (0) is real was computed.
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.
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.
In this work, we introduce and investigate an interesting subclass K-s(h) of analytic and close-to-convex functions in the open unit disk U. For functions belonging to the class K-s(h), we derive several properties in...
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In this work, we introduce and investigate an interesting subclass K-s(h) of analytic and close-to-convex functions in the open unit disk U. For functions belonging to the class K-s(h), we derive several properties including (for example) the coefficient bounds as well as the distortion and growth theorems. The various results presented here would generalize many known results. (c) 2010 Elsevier Ltd. All rights reserved.
The class of close-to-convex functions are univalent and so its subclasses. For normalised analytic functions defined on the unit disk, four subclasses of close-to-convex functions are considered and Hermitian-Toeplit...
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The class of close-to-convex functions are univalent and so its subclasses. For normalised analytic functions defined on the unit disk, four subclasses of close-to-convex functions are considered and Hermitian-Toeplitz determinants for these classes are investigated. All the results presented in this article are sharp.
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.
Let f is an element of S, f be a close-to-convex function, f(k) (z) = [f (z(k))](1/k). The relative growth of successive coefficients of f(k) (z) is investigated. The sharp estimate of parallel toc(n+1)\ - \c(n)parall...
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Let f is an element of S, f be a close-to-convex function, f(k) (z) = [f (z(k))](1/k). The relative growth of successive coefficients of f(k) (z) is investigated. The sharp estimate of parallel toc(n+1)\ - \c(n)parallel to is obtained by using the method of the subordination function. (C) 2003 Published by Elsevier Inc.
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.
The authors make use of the Alexander integral transforms of certain analytic functions (which are starlike or convex of positive order) with a view to investigating the construction of sense-preserving, univalent, an...
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The authors make use of the Alexander integral transforms of certain analytic functions (which are starlike or convex of positive order) with a view to investigating the construction of sense-preserving, univalent, and close-to-convex harmonic functions.
The logarithmic coefficients gamma(n) of an analytic and univalent function f in the unit disk D = {z is an element of C : vertical bar z vertical bar < 1} with the normalization f(0) = 0 = f'(0) - 1 are define...
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The logarithmic coefficients gamma(n) of an analytic and univalent function f in the unit disk D = {z is an element of C : vertical bar z vertical bar < 1} with the normalization f(0) = 0 = f'(0) - 1 are defined by log f(z)/z = 2 Sigma(infinity)(n=1) gamma(n)z(n). Recently, D. K. Thomas [Proc. Amer. Math. Soc. 144 (2016), 1681-1687] proved that vertical bar gamma(3)vertical bar <= 7/12 for functions in a subclass of close-to-convex functions (with argument 0) and claimed that the estimate is sharp by providing a form of an extremal function. In the present paper, we point out that such extremal functions do not exist and the estimate is not sharp by providing a much more improved bound for the whole class of close-to-convex functions (with argument 0). We also determine a sharp upper bound of vertical bar gamma(3)vertical bar for close-to-convex functions (with argument 0) with respect to the Koebe function.
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