scholarly journals On Convex Functions Associated with Symmetric Cardioid Domain

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2321
Author(s):  
Sarfraz Nawaz Malik ◽  
Mohsan Raza ◽  
Qin Xin ◽  
Janusz Sokół ◽  
Rabbiya Manzoor ◽  
...  
Keyword(s):  
Real Axis ◽  
Convex Functions ◽  
Analytic Functions ◽  
Geometrical Structures ◽  
Ongoing Research ◽  
Image Domain ◽  
Geometrical Properties

The geometry of the image domain plays an important role in the characterization of analytic functions. Therefore, for a comprehensive and detailed study of these functions, a thorough analysis of the geometrical properties of their domains is of prime interest. In this regard, new geometrical structures are introduced and studied as an image domain and then their subsequent analytic functions are defined. Inspired and motivated by ongoing research, Malik et al. introduced a very innovative domain named the cardioid domain, which is symmetric about a real axis. Extending the same work on this symmetric cardioid domain, in this article, we provide a deeper analysis and define and study the convex functions associated with the symmetric cardioid domain, named cardio-convex functions.

On the Radius of Curvature for Convex Analytic Functions

1970 ◽  
Vol 22 (3) ◽  
pp. 486-491 ◽  
Author(s):  
Paul Eenigenburg
Keyword(s):  
Real Axis ◽  
Jordan Curve ◽  
Convex Functions ◽  
Analytic Functions ◽  
Tangent Line ◽  
Positive Real Axis ◽  
Radius Of Curvature ◽  
Arc Length ◽  
Positive Real ◽  
Image Position

Definition 1.1. Let be analytic for |z| < 1. If ƒ is univalent, we say that ƒ belongs to the class S.Definition 1.2. Let ƒ ∈ S, 0 ≦ α < 1. Then ƒ belongs to the class of convex functions of order α, denoted by Kα, provided(1)and if > 0 is given, there exists Z0, |Z0| < 1, such thatLet ƒ ∈ Kα and consider the Jordan curve ϒτ = ƒ(|z| = r), 0 < r < 1. Let s(r, θ) measure the arc length along ϒτ; and let ϕ(r, θ) measure the angle (in the anti-clockwise sense) that the tangent line to ϒτ at ƒ(reiθ) makes with the positive real axis.

scholarly journals On starlike functions associated with cardioid domain

2021 ◽  
Vol 109 (123) ◽  
pp. 95-107
Author(s):  
Saira Zainab ◽  
Mohsan Raza ◽  
Janusz Sokół ◽  
Sarfraz Malik
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Function Theory ◽  
Starlike Functions ◽  
Geometric Function Theory ◽  
Geometrical Structures ◽  
Image Domain ◽  
Geometric Function ◽  
Comprehensive Study

Analytic functions are characterized by the geometry of their image domains. That?s why, geometry of image domain is of substantial importance to have a comprehensive study of analytic functions. To introduce and study new geometrical structures as image domain and to define their subsequent analytic functions is an ongoing part of research in geometric function theory. We introduced a new domain named as cardioid domain and defined the corresponding analytic function, see [14]. Here we further study the cardioid domain, to define and study starlike functions associated with cardioid domain.

Successive coefficients of close-to-convex functions

2020 ◽  
Vol 32 (5) ◽  
pp. 1131-1141 ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Real Axis ◽  
Convex Functions ◽  
Positive Direction ◽  
The Real ◽  
Coefficient Problems ◽  
The Difference

AbstractIn this paper we discuss coefficient problems for functions in the class {{\mathcal{C}}_{0}(k)}. This family is a subset of {{\mathcal{C}}}, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate {|a_{n+1}|-|a_{n}|} and {|a_{n}|}. Moreover, it is proved that {\operatorname{Re}\{a_{n}\}\geq 0} for all {f\in{\mathcal{C}}_{0}(k)}.

scholarly journals Quasi-Hadamard Product of Certainω-Starlike andω-Convex Functions with respect to Symmetric Points

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Huo Tang ◽  
Guan-Tie Deng
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Symmetric Points

The main purpose of this paper is to derive some results associated with the quasi-Hadamard product of certainω-starlike andω-convex univalent analytic functions with respect to symmetric points.

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Fekete–Szegö problem for certain subclasses of analytic functions

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Halit Orhan ◽  
Erhan Deniz ◽  
Murat Çağlar
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractIn this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order

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