Fuzzy differential subordination and superordination results for the Mittag-Leffler type Pascal distribution

Abstract

In this paper, we derive several fuzzy differential subordination and fuzzy differential superordination results for analytic functions $ \mathcal{M}_{\xi, \beta}^{s, \gamma} $, which involve the extended Mittag-Leffler function and the Pascal distribution series. We also investigate and introduce a class $ \mathcal{MB}_{\xi, \beta}^{F, s, \gamma}(\rho) $ of analytic and univalent functions in the open unit disc $ \mathcal{D} $ by employing the newly defined operator $ \mathcal{M}_{\xi, \beta}^{s, \gamma} $. We determine a specific relationship of inclusion for this class. Further, we establish prerequisites for a function role in serving as both the fuzzy dominant and fuzzy subordinant of the fuzzy differential subordination and superordination, respectively. Some novel results that are sandwich-type can be found here.

Keywords

• analytic function
• fuzzy differential subordinations and fuzzy differential superordinations
• mittag-leffler functions
• mittag-leffler type pascal distribution
• sandwich-type results