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 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.

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 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 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 subclass of analytic functions defined by subordination

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3307-3318
Author(s):  
Nirupam Ghosh ◽  
A. Vasudevarao
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Open Problems ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with some open problems proposed by Q.H. Xu et al.([20], [21]). An application of Jack lemma for certain subclass of starlike functions has been discussed.

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 ESTIMATES FOR SOME CLASSES OF FUNCTIONS ASSOCIATED WITH -FUNCTION THEORY

2017 ◽  
Vol 95 (3) ◽  
pp. 446-456 ◽  
Author(s):  
SARITA AGRAWAL
Keyword(s):  
Convex Functions ◽  
Representation Theorem ◽  
Function Theory ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Coefficient Estimates

For every $q\in (0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach problem for the class of $q$-convex functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$. In addition, we consider the Fekete–Szegö problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to two conjectures for the class of $q$-starlike functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$.

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 Research on Geometric Mappings in Complex Systems Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yanyan Cui ◽  
Chaojun Wang ◽  
Sifeng Zhu
Keyword(s):  
Banach Spaces ◽  
Systems Analysis ◽  
Starlike Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Reinhardt Domains ◽  
Complex Order ◽  
Starlike Mappings

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclusions contain and generalize some known results.

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