Sandwich theorems involving fractional integrals applied to the $ q $ -analogue of the multiplier transformation

Shatha S. Alhily; Alina Alb Lupaş; Shatha S. Alhily; Alina Alb Lupaş

doi:10.3934/math.2024284

AIMS Mathematics

2024, Volume 9, Issue 3: 5850-5862. doi: 10.3934/math.2024284

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Sandwich theorems involving fractional integrals applied to the $ q $ -analogue of the multiplier transformation

Shatha S. Alhily ¹,
Alina Alb Lupaş ^{2
,
,}

1.
Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
2.
Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii street, 410087 Oradea, Romania

Received: 04 October 2023 Revised: 17 December 2023 Accepted: 10 January 2024 Published: 31 January 2024
MSC : 30C45

In this paper, the research discussed involves fractional calculus applied to a $ q $-operator. Fractional integrals applied to the $ q $-analogue of the multiplier transformation gives a new operator, and the research is conducted applying the differential subordination and superordination theories. The best dominant and the best subordinant are obtained by the theorems and corollaries discussed. Combining the results from the both theories, sandwich-type results are presented as a conclusion of this research.
Citation: Shatha S. Alhily, Alina Alb Lupaş. Sandwich theorems involving fractional integrals applied to the $ q $ -analogue of the multiplier transformation[J]. AIMS Mathematics, 2024, 9(3): 5850-5862. doi: 10.3934/math.2024284

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Abstract

In this paper, the research discussed involves fractional calculus applied to a $ q $-operator. Fractional integrals applied to the $ q $-analogue of the multiplier transformation gives a new operator, and the research is conducted applying the differential subordination and superordination theories. The best dominant and the best subordinant are obtained by the theorems and corollaries discussed. Combining the results from the both theories, sandwich-type results are presented as a conclusion of this research.

References

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