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

Madan Mohan Soren; Luminiţa-Ioana Cotîrlǎ; Madan Mohan Soren; Luminiţa-Ioana Cotîrlǎ

doi:10.3934/math.20241023

AIMS Mathematics

2024, Volume 9, Issue 8: 21053-21078. doi: 10.3934/math.20241023

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Research article

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

Madan Mohan Soren ¹,
Luminiţa-Ioana Cotîrlǎ ^{2
,
,}

1.
Department of Mathematics, Berhampur University, Bhanja Bihar 760007, Odisha, India
2.
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca 400114, Romania

Received: 11 March 2024 Revised: 15 May 2024 Accepted: 21 May 2024 Published: 28 June 2024
MSC : 30C45, 30C80, 33E12

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.
Citation: Madan Mohan Soren, Luminiţa-Ioana Cotîrlǎ. Fuzzy differential subordination and superordination results for the Mittag-Leffler type Pascal distribution[J]. AIMS Mathematics, 2024, 9(8): 21053-21078. doi: 10.3934/math.20241023

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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.

References

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