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Some properties of a class of holomorphic functions associated with tangent function

Khan Muhammad Ghaffar, Mashwani Wali Khan, Salleh Zabidin, Tchier Fairouz, Khan Bilal, Malik Sarfraz Nawaz

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230142

In this study, we define new class of holomorphic functions associated with tangent function. Furthermore, we examine the differential subordination implementation results related to Janowski and tangent functions. Also, we investigate some extreme point theorem and partial sums results, necessary and sufficient conditions, convex combination, closure theorem, growth and distortion bounds, and radii of close-to-starlikeness and starlikeness for this newly defined functions class of holomorphic functions.

On q-analogue of Janowski-type starlike functions with respect to symmetric points

Khan Muhammad Ghaffar, Ahmad Bakhtiar, Khan Raees, Zubair Muhammad, Salleh Zabidin

Demonstratio Mathematica

2021

Vol. 54, nr 1

37--46

The main objective of the present paper is to define a class of q-starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.