scholarly journals Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 440 ◽  
Author(s):  
Muhammad Naeem ◽  
Saqib Hussain ◽  
Shahid Khan ◽  
Tahir Mahmood ◽  
Maslina Darus ◽  
...  
Keyword(s):  
Convex Functions ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
Conic Domain ◽  
New Findings ◽  
Convolution Properties

Certain new classes of q-convex and q-close to convex functions that involve the q-Janowski type functions have been defined by using the concepts of quantum (or q-) calculus as well as q-conic domain Ω k , q [ λ , α ] . This study explores some important geometric properties such as coefficient estimates, sufficiency criteria and convolution properties of these classes. A distinction of new findings with those obtained in earlier investigations is also provided, where appropriate.

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 $0\leq \unicode[STIX]{x1D6FC}<1$.

Some properties of a subclass of uniformly convex functions with negative coefficients

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions

AbstractThe aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass

Starlike and convex functions with respect to symmetric conjugate points involving conical domain

2018 ◽  
Vol 68 (1) ◽  
pp. 89-102
Author(s):  
C. Ramachandran ◽  
R. Ambrose Prabhu ◽  
Srikandan Sivasubramanian
Keyword(s):  
Convex Functions ◽  
Domain Growth ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Interesting Application ◽  
New Class ◽  
Starlike And Convex Functions ◽  
Distortion Estimates ◽  
Symmetric Points

AbstractEnough attentions to domains related to conical sections has not been done so far although it deserves more. Making use of the conical domain the authors have defined a new class of starlike and Convex Functions with respect to symmetric points involving the conical domain. Growth and distortion estimates are studied with convolution using domains bounded by conic regions. Certain coefficient estimates are obtained for domains bounded by conical region. Finally interesting application of the results are also highlighted for the function Ωk,βdefined by Noor.

Geometric properties for a family of holomorphic functions associated with Wanas operator defined on complex Hilbert space

2020 ◽  
pp. 2150122
Author(s):  
Abbas Karem Wanas ◽  
Junesang Choi ◽  
Nak Eun Cho
Keyword(s):  
Hilbert Space ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

By making use of Wanas operator, we aim to introduce and investigate a certain family of univalent holomorphic functions with negative coefficients defined on complex Hilbert space. We present some important geometric properties of this family such as coefficient estimates, convexity, distortion and growth, radii of starlikeness and convexity. We also discuss the extreme points for functions belonging to this family.

scholarly journals Uniformly Alpha-Quasi-Convex Functions Defined by Janowski Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shahid Mahmood ◽  
Sarfraz Nawaz Malik ◽  
Sumbal Farman ◽  
S. M. Jawwad Riaz ◽  
Shabieh Farwa
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Janowski Functions ◽  
Convolution Properties ◽  
Inclusion Results

In this work, we aim to introduce and study a new subclass of analytic functions related to the oval and petal type domain. This includes various interesting properties such as integral representation, sufficiency criteria, inclusion results, and the convolution properties for newly introduced class.

scholarly journals Convolution Properties for Some Subclasses of Meromorphic Functions of Complex Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa ◽  
H. M. Zayed
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Convolution Properties

Making use of the operatorLυfor functions of the formfz=1/z+∑k=1∞akzk-1, which are analytic in the punctured unit discU∗={z:z∈Cand0<|z|<1}=U∖{0}, we introduce two subclasses of meromorphic functions and investigate convolution properties, coefficient estimates, and containment properties for these subclasses.

Higher Order Close-to-Convex Functions related with Conic Domain

2014 ◽  
Vol 8 (5) ◽  
pp. 2455-2463 ◽  
Author(s):  
Khalida Inayat Noor ◽  
Muhammad Aslam Noor
Keyword(s):  
Convex Functions ◽  
Higher Order ◽  
Conic Domain

scholarly journals Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

2012 ◽  
Vol 25 (3) ◽  
pp. 344-351 ◽  
Author(s):  
Rosihan M. Ali ◽  
See Keong Lee ◽  
V. Ravichandran ◽  
Shamani Supramaniam
Keyword(s):  
Convex Functions ◽  
Coefficient Estimates ◽  
Starlike And Convex Functions

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).

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