Geometric applications for meromorphic functions involving $ \mathfrak{q} $-linear operators

Ekram E. Ali; Rabha M. El-Ashwah; Abeer M. Albalahi; Ekram E. Ali; Rabha M. El-Ashwah; Abeer M. Albalahi

doi:10.3934/math.20251360

AIMS Mathematics

2025, Volume 10, Issue 12: 30990-31009. doi: 10.3934/math.20251360

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Geometric applications for meromorphic functions involving $ \mathfrak{q} $-linear operators

1.
Department of Mathematics, Faculty 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.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Received: 12 November 2025 Revised: 16 December 2025 Accepted: 29 December 2025 Published: 31 December 2025
MSC : 26A33, 30C45, 30C50, 30C80

This paper investigated the $ \mathfrak{q} $-analogue of the multiplier-Ruscheweyh operator acting on meromorphic analytic functions, denoted by $ \mathfrak{D}_{\mathfrak{q}, \varepsilon }^{r}(\varkappa, \varrho). $ By applying tools from $ \mathfrak{q} $-calculus together with the principle of subordination, we developed several analytical results that deepened the understanding of geometric function theory (GFT) in the setting of meromorphic functions. The study focused on constructing new subclasses of meromorphic univalent functions associated with the operator $ \mathfrak{D} _{\mathfrak{q}, \varepsilon }^{r}(\varkappa, \varrho), $ characterized by $ \mathfrak{q} $-starlikeness, $ \mathfrak{q} $-convexity, and related geometric classes. Various inclusion relationships, differential inequalities, and integral preservation properties were examined to establish the structural behavior of these families of functions. The findings generalized and unified several existing results in the literature concerning different operators and extended their applications to broader contexts within meromorphic function theory with $ \mathfrak{q} $-calculus operator.
Citation: Ekram E. Ali, Rabha M. El-Ashwah, Abeer M. Albalahi. Geometric applications for meromorphic functions involving $ \mathfrak{q} $-linear operators[J]. AIMS Mathematics, 2025, 10(12): 30990-31009. doi: 10.3934/math.20251360

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Abstract

This paper investigated the $ \mathfrak{q} $-analogue of the multiplier-Ruscheweyh operator acting on meromorphic analytic functions, denoted by $ \mathfrak{D}_{\mathfrak{q}, \varepsilon }^{r}(\varkappa, \varrho). $ By applying tools from $ \mathfrak{q} $-calculus together with the principle of subordination, we developed several analytical results that deepened the understanding of geometric function theory (GFT) in the setting of meromorphic functions. The study focused on constructing new subclasses of meromorphic univalent functions associated with the operator $ \mathfrak{D} _{\mathfrak{q}, \varepsilon }^{r}(\varkappa, \varrho), $ characterized by $ \mathfrak{q} $-starlikeness, $ \mathfrak{q} $-convexity, and related geometric classes. Various inclusion relationships, differential inequalities, and integral preservation properties were examined to establish the structural behavior of these families of functions. The findings generalized and unified several existing results in the literature concerning different operators and extended their applications to broader contexts within meromorphic function theory with $ \mathfrak{q} $-calculus operator.

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