• Corpus ID: 214743358

Analytic representation of the generalized Pascal snail and its applications

@article{Kanas2020AnalyticRO,
  title={Analytic representation of the generalized Pascal snail and its applications},
  author={Stanislawa Kanas and Vali Soltani Masih},
  journal={arXiv: Complex Variables},
  year={2020}
}
We find an unifying approach to the analytic representation of the domain bounded by a generalized Pascal snail. Special cases as Pascal snail, Both leminiscate, conchoid of the Sluze and a disc are included. The behavior of functions related to generalized Pascal snail are demonstrated. 

References

SHOWING 1-10 OF 16 REFERENCES
On λ-pseudo-starlike functions
In this paper, we isolate some new, interesting classes of λ -pseudo-starlike univalent functions in the open unit disk E = {z ∈ C : |z| < 1} . Some characterizations of them are obtained and
On a Subclass of Strongly Starlike Functions Associated with Exponential Function
Abstract. Let S ∗ e denote the class of analytic functions f in the open unit disk normalized by f (0) = f ′(0)−1= 0 and satisfying the condition z f′(z)/ f (z)≺ ez for |z| < 1. The structural
On Booth Lemniscate and Hadamard Product of Analytic Functions
Abstract In [RUSCHEWEYH, S.-SHEIL-SMALL, T.: Hadamard product of schlicht functions and the Poyla-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135] the authors proved the
Constrained coefficients problem for generalized typically real functions
For let denote the class of generalized typically real functions i.e. the class of functions of a form where , and is the unique probability measure on the interval . For the same range of
ON CONFORMAL REPRESENTATIONS OF THE INTERIOR OF AN ELLIPSE
We consider the conformal mappings f and g of the unit disk onto the inside of an ellipse with foci at 1 so that f(0) = 0, f 0 (0) > 0, g(0) = 1 and g 0 (0) > 0. The main purpose of this article is
Coefficients problems for families of holomorphic functions related to hyperbola
Abstract We consider a family of analytic and normalized functions that are related to the domains ℍ(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the
Grid generation using lemniscates with two foci
Some properties associated to a certain class of starlike functions
Abstract Let 𝓐 denote the family of analytic functions f with f(0) = f′(0) – 1 = 0, in the open unit disk Δ. We consider a class Scs∗(α):=f∈A:zf′(z)f(z)−1≺z1+α−1z−αz2,z∈Δ, $$\begin{array}{}
Generalized Typically Real Functions
Let $f(z) = z+a_2 z^2+\cdots$ be regular in the unit disk  and real valued if and only if $z$ is real and $|z| < 1$. Then $f$ is said to be typically real function. Rogosinski found the necessary and
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