A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

Date

2021

Authors

Srivastava, H.M.
Khan, Nazar
Khan, Shahid
Zahoor Ahmad, Qazi
Khan, Bilal

Journal Title

Journal ISSN

Volume Title

Publisher

Mathematics

Abstract

In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, a representation theorem, and a distortion theorem. We also apply a generalized q-Bernardi–Libera–Livingston integral operator to examine the closure properties and coefficient bounds. Furthermore, we highlight some known consequences of our main results. In the concluding part of the article, we have finally reiterated the well-demonstrated fact that the results presented in this article can easily be rewritten as the so-called (p,q)-variations by making some straightforward simplifications, and it will be an inconsequential exercise, simply because the additional parameter p is obviously unnecessary.

Description

Keywords

univalent functions, harmonic functions, q-derivative (or q-difference) operator

Citation

Srivastava, H. M., Khan, N., Khan, S., Zahoor Ahmad, Q., & Khan, B. (2021). A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator. Mathematics, 9(15), 1-14. https://doi.org/10.3390/math9151812.