Coefficient bounds for certain subclasses of close-to-convex functions of complex order

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6401-6408 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Differential Equation ◽  
Convex Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Type Differential Equation

In this paper, we determine the coefficient bounds for functions in certain subclasses of close-to-convex functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy-Euler-type differential equation of order m. Relevant connections of some of the results obtained with those in earlier works are also provided.

On coefficient bounds of some new subfamilies of close-to-convex functions of complex order related to generalized differential operator

2018 ◽  
Vol 13 (03) ◽  
pp. 2050049
Author(s):  
Serap Bulut ◽  
Manzoor Hussain ◽  
Abdul Ghafoor
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Convex Functions ◽  
Coefficient Bounds ◽  
Homogeneous Differential Equation ◽  
Complex Order ◽  
Coefficient Inequalities ◽  
Generalized Differential

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.

scholarly journals Coefficient Bounds for Certain Subclasses of Analytic Functions Defined by Komatu Integral Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Serap Bulut
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Analytic Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Type Differential Equation

We determine the coeffcient bounds for functions in certain subclasses of analytic functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler type differential equation of orderm. Relevant connections of some of the results obtained with those in earlier works are also provided.

scholarly journals On coefficient bounds of certain subfamilies of close-to-convex functions of complex order defined by Sãlãgean derivatives

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 99-103 ◽  
Author(s):  
Wasim Ul-Haq ◽  
Shabana Manzar
Keyword(s):  
Differential Equation ◽  
Recent Work ◽  
Convex Functions ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Homogeneous Differential Equation ◽  
Complex Order

Motivated from the recent work of Srivastava et al. (H.M. Srivastava, Qing-Hua Xu, Guang-Ping Wu, Coefficient estimates for certain subclasses of spiral-like functions of complex order, 23 (2010) 763-768), we aim to determine the coefficient estimates for functions in certain subclasses of close-to-convex and related functions of complex order, which are here defined by means of S?l?gean derivative operator and Cauchy-Euler type non-homogeneous differential equation. Several interesting consequences of our results are also observed.

scholarly journals Coefficient estimates for certain subfamilies of close-to-convex functions of complex order

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1139-1142 ◽  
Author(s):  
Wasim Ul-Haq ◽  
Attiya Nazneen ◽  
Nasir Rehman
Keyword(s):  
Differential Equation ◽  
Recent Work ◽  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Coefficient Bounds ◽  
Homogeneous Differential Equation ◽  
Complex Order ◽  
Appl Math

Motivated from the recent work of Srivastava et al. (H.M. Srivastava, O. Alt?ntas?, S. K. Serenbay, Coefficient bounds for certain subclasses of starlike functions of complex order, Appl. Math. Lett. 24(2011)1359-1363.), we aim to determine the coefficient estimates for functions in certain subclasses of close-to-convex and related functions of complex order, which are here defined by means of Cauchy-Euler type non-homogeneous differential equation. Several interesting consequences of our results are also observed.

scholarly journals Coefficient bounds for some families of starlike and convex functions of complex order

2007 ◽  
Vol 20 (12) ◽  
pp. 1218-1222 ◽  
Author(s):  
Osman Altıntaş ◽  
Hüseyin Irmak ◽  
Shigeyoshi Owa ◽  
H.M. Srivastava
Keyword(s):  
Convex Functions ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions ◽  
Complex Order

scholarly journals On close-to-convex functions of complex order

1990 ◽  
Vol 13 (2) ◽  
pp. 321-330 ◽  
Author(s):  
H. S. Al-Amiri ◽  
Thotage S. Fernando
Keyword(s):  
Convex Functions ◽  
Nonnegative Integer ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Covering Theorems

The classS*(b)of starlike functions of complex orderbwas introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the classK(b)of functions close-to-convex of complex orderb,b≠0and its generalization, the classesKn(b)wherenis a nonnegative integer. HereS*(b)⊂K(b)=K0(b). Sharp coefficient bounds are determined forKn(b)as well as several sufficient conditions for functions to belong toKn(b). The authors also obtain some distortion and covering theorems forKn(b)and determine the radius of the largest disk in which everyf∈Kn(b)belongs toKn(1). All results are sharp.

scholarly journals Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

2021 ◽  
pp. 49-76
Author(s):  
Faroze Ahmad Malik ◽  
Nusrat Ahmed Dar ◽  
Chitaranjan Sharma
Keyword(s):  
Convex Functions ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Integral Means ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Special Cases ◽  
The Family

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

scholarly journals On a Subclass of Harmonic Convex Functions of Complex Order

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
N. Magesh ◽  
S. Mayilvaganan
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Closure Property ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Distortion Bounds ◽  
Order Coefficient ◽  
Harmonic Convex

We introduce and study a subclass of harmonic convex functions of complex order. Coefficient bounds, extreme points, distortion bounds, convolution conditions, and convex combination are determined for functions in this class. Further, we obtain the closure property of this class under integral operator.

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