Third-Order Differential Subordination Results for Meromorphic Functions Associated with the Inverse of the Legendre Chi Function via the Mittag-Leffler Identity

Adel Salim Tayyah, Waggas Galib Atshan and Georgia Irina Oros ()
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Adel Salim Tayyah: Department of Computer Science, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah 58002, Iraq
Waggas Galib Atshan: Department of Mathematics, College of Science, University of Al-Qadisiyah, Diwaniyah 58002, Iraq
Georgia Irina Oros: Department of Mathematics and Computer Science, University of Oradea, Universitatii 1, 410087 Oradea, Romania

Mathematics, 2025, vol. 13, issue 13, 1-18

Abstract: In this paper, we derive novel results concerning third-order differential subordinations for meromorphic functions, utilizing a newly defined linear operator that involves the inverse of the Legendre chi function in conjunction with the Mittag-Leffler identity. To establish these results, we introduce several families of admissible functions tailored to this operator and formulate sufficient conditions under which the subordinations hold. Our study presents three fundamental theorems that extend and generalize known results in the literature. Each theorem is accompanied by rigorous proofs and further supported by corollaries and illustrative examples that validate the applicability and sharpness of the derived results. In particular, we highlight special cases and discuss their implications through both analytical evaluations and graphical interpretations, demonstrating the strength and flexibility of our framework. This work contributes meaningfully to the field of geometric function theory by offering new insights into the behavior of third-order differential operators acting on p -valent meromorphic functions. Furthermore, the involvement of the Mittag-Leffler function positions the results within the broader context of fractional calculus, suggesting potential for applications in the mathematical modeling of complex and nonlinear phenomena. We hope this study stimulates further research in related domains.

Keywords: meromorphic functions; third-order differential subordination; Legendre Chi Function; Mittag-Leffler Function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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