@article{Ali2024, 
author = {Ekram E. Ali and Nicoleta Breaz and Rabha M. El-Ashwah},
title = {Subordinations and superordinations studies using    q-difference operator},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {18143-18162},
keywords = {analytic function, differential subordination, superordination, q-difference operator, q-analogue Catas operator, q-analogue of Ruscheweyh operator},
url = {https://www.sciopen.com/article/10.3934/math.2024886},
doi = {10.3934/math.2024886},
abstract = {The results of this work belong to the field of geometric function theory, being based on differential subordination methods. Using the idea of the        q  -calculus operators, we define the        q  -analogue of the multiplier- Ruscheweyh operator of a specific family of linear operators,        I                  q            ,      μ              s        (  λ  ,  ℓ  )  . Our major goal is to build and investigate some analytic function subclasses using        I                  q            ,      μ              s        (  λ  ,  ℓ  ). Also, some differential subordination and superordination results are obtained. Moreover, based on the new theoretical results, several examples are constructed. For every differential superordination under investigation, the best subordinant is provided.}
}