On The Third-Order Complex Differential Inequalities of <i>ξ</i>-Generalized-Hurwitz–Lerch Zeta Functions

Abstract

In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some applications of the third-order differential subordination for a newly defined linear operator that includes ξ -Generalized-Hurwitz–Lerch Zeta functions (GHLZF). These outcomes are derived by investigating the appropriate classes of admissible functions.

Keywords

• holomorphic function
• univalent function
• <i>p</i>-valent function
• convolution product
• <i>ξ</i>-Generalized Hurwitz–Lerch Zeta function
• differential subordination