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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.

On Janowski harmonic functions

Dziok J.

Journal of Applied Analysis

2015

Vol. 21, nr 2

99--107

In this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.