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Keywords = Ma-Minda class

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14 pages, 889 KiB  
Article
On a New Ma-Minda Class of Analytic Functions Created by a Roulette Curve Formula
by Ibtisam Aldawish and Rabha W. Ibrahim
Symmetry 2023, 15(10), 1913; https://doi.org/10.3390/sym15101913 - 13 Oct 2023
Viewed by 1513
Abstract
It is well known that there are two important classes of analytic functions of Ma-Minda type (MMT): Ma-Minda starlike and Ma-Minda convex functions. In this work, we suggest a new class of analytic functions, which is normalized in the open unit disk. The [...] Read more.
It is well known that there are two important classes of analytic functions of Ma-Minda type (MMT): Ma-Minda starlike and Ma-Minda convex functions. In this work, we suggest a new class of analytic functions, which is normalized in the open unit disk. The suggested class is generated by a roulette curve formula, which satisfies the symmetric behavior in the open unit disk. A roulette curve is shaped as the path outlined by the sum of two complex numbers, each affecting at a uniform rapidity in a circle. Special cases are illustrated involving special functions. Graphics of the curve are illustrated by using Mathematica 13.3. Full article
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16 pages, 693 KiB  
Article
Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses
by Aaisha Farzana Habibullah, Muthusamy Palani Jeyaraman and Teodor Bulboacă
Mathematics 2022, 10(16), 2879; https://doi.org/10.3390/math10162879 - 11 Aug 2022
Viewed by 1533
Abstract
For a function p analytic in the open unit disc and satisfying p(0)=1, we prove certain subordination implications of the first order differential subordination 1+zp(z)1+Mz [...] Read more.
For a function p analytic in the open unit disc and satisfying p(0)=1, we prove certain subordination implications of the first order differential subordination 1+zp(z)1+Mz, which provides sufficient conditions for a function to belong to various subclasses of Ma-Minda starlike functions. The pre-Schwarzian norm estimate and inclusion criteria for certain subclasses of analytic function are also obtained. Additionally, using Gronwall’s inequality we give a sufficient condition for a normalized function to belong to a class of functions with bounded arguments that extends the class of strongly α-Bazilevič functions of order γ studied by Gao in 1996. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)
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