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 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

Coefficient bounds for a subclass of starlike functions of complex order

2011 ◽  
Vol 218 (3) ◽  
pp. 693-698
Author(s):  
Murat Çağlar ◽  
Erhan Deniz ◽  
Halit Orhan
Keyword(s):  
Starlike Functions ◽  
Coefficient Bounds ◽  
Complex Order

scholarly journals Estimates for coefficients of certain analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3539-3552 ◽  
Author(s):  
V. Ravichandran ◽  
Shelly Verma
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Coefficient Problem ◽  
Inverse Coefficient Problem ◽  
Coefficient Bounds ◽  
Inverse Functions ◽  
Inverse Coefficient

For -1 ? B ? 1 and A > B, let S*[A,B] denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions f defined by the subordination z f'(z)/f(z)< (1+Az)/(1+Bz) (?z?<1). For -1 ? B ? 1 < A, we investigate the inverse coefficient problem for functions in the class S*[A,B] and its meromorphic counter part. Also, for -1 ? B ? 1 < A, the sharp bounds for first five coefficients for inverse functions of generalized Janowski convex functions are determined. A simple and precise proof for inverse coefficient estimations for generalized Janowski convex functions is provided for the case A = 2?-1(?>1) and B = 1. As an application, for F:= f-1, A = 2?-1 (?>1) and B = 1, the sharp coefficient bounds of F/F' are obtained when f is a generalized Janowski starlike or generalized Janowski convex function. Further, we provide the sharp coefficient estimates for inverse functions of normalized analytic functions f satisfying f'(z)< (1+z)/(1+Bz) (?z? < 1, -1 ? B < 1).

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.

scholarly journals Bounded Doubly Close-to-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dorina Răducanu
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Bounds ◽  
New Class ◽  
Radius Of Convexity ◽  
Distortion Theorems

We consider a new classCC(α,β)of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the classCC(α,β)are investigated. A corresponding class of doubly close-to-starlike functionsS*S(α,β)is also considered.

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 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 The radius of starlikeness for convex functions of complex order

2004 ◽  
Vol 2004 (45) ◽  
pp. 2423-2428 ◽  
Author(s):  
Yaşar Polatoglu ◽  
Metin Bolcal ◽  
Arzu Şen
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Radius Of Starlikeness ◽  
Complex Order

We will give the relation between the class of Janowski starlike functions of complex order and the class of Janowski convex functions of complex order. As a corollary of this relation, we obtain the radius of starlikeness for the class of Janowski convex functions of complex order.

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