@article{Zhang2022, 
author = {Caihuan Zhang and Shahid Khan and Aftab Hussain and Nazar Khan and Saqib Hussain and Nasir Khan},
title = {Applications of    q-difference symmetric operator in harmonic univalent functions},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {667-680},
keywords = {univalent functions, harmonic functions, symmetric q-derivative operator, symmetric Salagean q-differential operator},
url = {https://www.sciopen.com/article/10.3934/math.2022042},
doi = {10.3934/math.2022042},
abstract = {In this paper, for the first time, we apply symmetric    q -calculus operator theory to define symmetric Salagean    q-differential operator. We introduce a new class                                H                ~                    q              m            (    α    )   of harmonic univalent functions    f associated with newly defined symmetric Salagean    q-differential operator for complex harmonic functions. A sufficient coefficient condition for the functions    f to be sense preserving and univalent and in the same class is obtained. It is proved that this coefficient condition is necessary for the functions in its subclass                                                          H                        ~                                    q                          m                            (        α        )              ¯   and obtain sharp coefficient bounds, distortion theorems and covering results. Furthermore, we also highlight some known consequence of our main results.}
}