New results about fuzzy $ \mathbf{\gamma } $-convex functions connected with the $ \mathfrak{q} $-analogue multiplier-Noor integral operator

Ekram E. Ali; Miguel Vivas-Cortez; Rabha M. El-Ashwah; Ekram E. Ali; Miguel Vivas-Cortez; Rabha M. El-Ashwah

doi:10.3934/math.2024263

AIMS Mathematics

2024, Volume 9, Issue 3: 5451-5465. doi: 10.3934/math.2024263

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Research article

New results about fuzzy $ \mathbf{\gamma } $-convex functions connected with the $ \mathfrak{q} $-analogue multiplier-Noor integral operator

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
2.
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42521, Egypt
3.
Facultad de Ciencias Exactas y Naturales, Escuela de Ciencias Fisicas y Matematicas, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076, Quito 170143, Ecuador
4.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Received: 07 November 2023 Revised: 25 December 2023 Accepted: 03 January 2024 Published: 29 January 2024
MSC : 30C45, 30C80

The features of analytical functions were mostly studied using a fuzzy subset and a $ \mathfrak{q} $-difference operator in this study, as we investigate many fuzzy differential subordinations related to the $ \mathfrak{q} $-analogue multiplier-Noor integral operator. By applying fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis, we create a few new subclasses of analytical functions. We define numerous classes related to the family of linear $ \mathfrak{q} $ -operators and introduce them. Here, we focus on the inclusion results and other integral features.
- analytic functions,
- fuzzy $ \mathfrak{q} $-starlike functions,
- fuzzy $ \mathfrak{q} $-convex functions
Citation: Ekram E. Ali, Miguel Vivas-Cortez, Rabha M. El-Ashwah. New results about fuzzy $ \mathbf{\gamma } $-convex functions connected with the $ \mathfrak{q} $-analogue multiplier-Noor integral operator[J]. AIMS Mathematics, 2024, 9(3): 5451-5465. doi: 10.3934/math.2024263

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Abstract

The features of analytical functions were mostly studied using a fuzzy subset and a $ \mathfrak{q} $-difference operator in this study, as we investigate many fuzzy differential subordinations related to the $ \mathfrak{q} $-analogue multiplier-Noor integral operator. By applying fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis, we create a few new subclasses of analytical functions. We define numerous classes related to the family of linear $ \mathfrak{q} $ -operators and introduce them. Here, we focus on the inclusion results and other integral features.

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