In this paper, we answer the questions raised in the paper [On the difference of inverse coefficients of univalent functions, Symmetry, 2020, 12(12), art. 2040, 14pp] by Sim and Thomas, and aim to verify the conjectur...
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In this paper, we answer the questions raised in the paper [On the difference of inverse coefficients of univalent functions, Symmetry, 2020, 12(12), art. 2040, 14pp] by Sim and Thomas, and aim to verify the conjecture posed therein in certain cases. For this purpose, we investigate sharp bounds on moduli difference of successive inverse coefficients for certain classes of close-to-convex functions.
In this paper, bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.
In this paper, bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.
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.
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.
Sharp upper and lower bounds of the Hermitian Toeplitz determinants of the second and third orders are found for various subclasses of close-to-convex functions.
Sharp upper and lower bounds of the Hermitian Toeplitz determinants of the second and third orders are found for various subclasses of close-to-convex functions.
In this paper, we define a new subclass of close-to-convex functions with respect to certain univalent functions studied by [Z. Peng and G. Zhong, Some properties for certain classes of univalent functions defined by ...
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In this paper, we define a new subclass of close-to-convex functions with respect to certain univalent functions studied by [Z. Peng and G. Zhong, Some properties for certain classes of univalent functions defined by differential inequalities, Acta Math. Sci. Ser. B (Engl. Ed.) 37(1) (2017) 69-78]. We find certain examples of functions belong to the class. Further, we give coefficient estimates, distortion theorem and some more results for this new subclass. Finally, we obtain radius of convexity for functions belong to the class.
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.
We aim to estimate coefficient inequalities for some new subfamilies of close-to-convex functions, which are here, defined by generalized differential operator and Cauchy-Euler type non-homogeneous differential equati...
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We aim to estimate coefficient inequalities for some new subfamilies of close-to-convex functions, which are here, defined by generalized differential operator and Cauchy-Euler type non-homogeneous differential equation. The results presented here would extend, unify and improve some recent results in literature.
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.
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.
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