A Study on q -Starlike Functions Connected with q -Extension of Hyperbolic Secant and Janowski Functions

Pengfei Bai, Adeel Ahmad, Akhter Rasheed, Saqib Hussain (), Huo Tang and Saima Noor
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Pengfei Bai: School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China
Adeel Ahmad: Department of Mathematics and Statistics, Hazara University Mansehra, Dhodial 21120, Pakistan
Akhter Rasheed: Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan
Saqib Hussain: Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan
Huo Tang: School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China
Saima Noor: Department of Mathematics and Statistics, College of science, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia

Mathematics, 2025, vol. 13, issue 13, 1-17

Abstract: This study introduces a novel subclass of q -starlike functions that is defined by the application of the q -difference operator and q -analogue of hyperbolic secant function. By making certain variations to the parameter “ q ”, the geometric interpretation of the domain hyperbolic secant function has also been discussed. The primary objective is to investigate and establish key results on the differential subordination of various orders within this newly defined class. Furthermore, convolution properties are explored and coefficient bounds are derived for these functions. A deeper analysis of these coefficients bounds unveils intriguing geometric insights and significant mathematical problems.

Keywords: analytic functions; q -Calculus; convolution; differential Subordination; secant hyperbolic function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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