Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

Saeed Islam,Ronnason Chinram,Bakhtiar Ahmad,Muhammad Ghaffar Khan,Muhammad Arif

doi:10.3390/math8101676

Saeed Islam, Ronnason Chinram + Show 3 more

Open Access

https://doi.org/10.3390/math8101676

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Abstract

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class.

Highlights

Introduction and DefinitionsTo understand all the concepts used in this article clearly we need to include and explain all the terms mentioned here
In [1,2], Miller and Mocanu generalized the ideas that consist of differential inequalities for real to complex valued functions that laid the foundations for a new theory, known as “the method of differential subordination or admissible functions method”
Utilizing the principle of subordinations, we have defined the family of q-starlike functions connected with a particular trigonometric function such as sine functions

Summary

Introduction and Definitions

To understand all the concepts used in this article clearly we need to include and explain all the terms mentioned here. In [1,2], Miller and Mocanu generalized the ideas that consist of differential inequalities for real to complex valued functions that laid the foundations for a new theory, known as “the method of differential subordination or admissible functions method”. 1+ Bz starlike functions; see [5] Some interesting problems such as convolution properties, coefficient inequalities, sufficient conditions, subordinates results and integral preserving were discussed recently in [6,7,8,9,10] for some of the generalized families associated with circular domains. The ratio f (z) lies in an eight-shaped region in the right half plane They investigated the inverse inclusion relations of this family with the already known subfamilies of analytic functions.

Major Contributions

Partial Sum Problems

Conclusions