Fuzzy differential subordination and superordination results for $ q $ -analogue of multiplier transformation

Alina Alb Lupaş; Shujaat Ali Shah; Loredana Florentina Iambor; Alina Alb Lupaş; Shujaat Ali Shah; Loredana Florentina Iambor

doi:10.3934/math.2023794

AIMS Mathematics

2023, Volume 8, Issue 7: 15569-15584. doi: 10.3934/math.2023794

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Research article

Fuzzy differential subordination and superordination results for $ q $ -analogue of multiplier transformation

1.
Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii street, 410087 Oradea, Romania
2.
Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, (QUEST) Nawabshah, 67450, Pakistan

Received: 09 February 2023 Accepted: 27 March 2023 Published: 27 April 2023
MSC : 30A20, 30C45, 34A40

In this paper the authors combine the quantum calculus applications regarding the theories of differential subordination and superordination with fuzzy theory. These results are established by means of an operator defined as the $ q $-analogue of the multiplier transformation. Interesting fuzzy differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc $ U $ which is defined and investigated here by using this $ q $-operator.
- convex function,
- differential operator,
- $ q $ -analogue operator,
- fuzzy differential subordination,
- fuzzy best dominant,
- fuzzy differential superordination,
- fuzzy best subordinant
Citation: Alina Alb Lupaş, Shujaat Ali Shah, Loredana Florentina Iambor. Fuzzy differential subordination and superordination results for $ q $ -analogue of multiplier transformation[J]. AIMS Mathematics, 2023, 8(7): 15569-15584. doi: 10.3934/math.2023794

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Abstract

In this paper the authors combine the quantum calculus applications regarding the theories of differential subordination and superordination with fuzzy theory. These results are established by means of an operator defined as the $ q $-analogue of the multiplier transformation. Interesting fuzzy differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc $ U $ which is defined and investigated here by using this $ q $-operator.

References

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