On The Third-Order Complex Differential Inequalities of ξ-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.

Geometrical Theory of Analytic Functions

“…Certain applications of third-order differential subordination for a newly defined linear operator that includes ξ-generalized Hurwitz-Lerch Zeta functions are considered by the authors Hiba Al-Janaby, Firas Ghanim, and Maslina Darus in [6]. A new generalized Noor-type linear integral operator for the class of p-valent functions is defined, and several outcomes concerning the use of third-order differential subordination for multivalent functions, including this operator, are presented.…”

“…Funding: The research presented in [3] was funded by the Concordia College Chemistry Endowment Fund. The research presented in [6] was funded by Universiti Kebangsaan Malaysia, grant number GUP-2019-032. The second author of [7] was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (No.…”

Third Order Differential Subordination for Analytic Functions Involving Convolution Operator

“…𝑓 ≺ 𝑔 𝑖𝑛 𝑈 𝑜𝑟 𝑔(𝑤) ≺ 𝑓(𝑤) , (𝑤 ∈ 𝑈), if there exists a Schwarz function 𝓀(𝑤) which (by definition) is analytic in U satisfies the following conditions (see [1][2][3][4][5][6][7][8][9] ), 𝓀(0) = 0 𝑎𝑛𝑑 |𝓀(𝑤)| < 1 for all (𝑤 ∈ 𝑈), such that 𝑓(𝑤) = 𝑔(𝓀(𝑤))…”

Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function

“…. Along with these, there are more remarkable diverse extensions and generalizations that contributed to the rise of new classes of the Hurwitz-Lerch Zeta function in ( [16][17][18][19][20][21][22][23][24][25][26]).…”