Applications of third order differential subordination and superordination involving generalized struve function

Abstract

In the present paper, we derive the third-order differential subordination and superordination results for some analytic univalent functions defined in the unit disc.These results are associated with generalized Struve functions and are obtained by considering suitable classes of admissible functions. As a consequence, the dual problems which yield the sandwich type relations are presented.

Third‐order differential subordinations for multivalent functions in the theory of source‐sink dynamics

“…which satisfies the conditions in (15) for fixed a ∈ C. Then, (26) leads to a +  p,𝜅,𝜎,𝜍 𝜇,𝛿,𝜁 𝑓 (z) ≺ q(z) for all z ∈ D and q is the best dominant of (26)…”

“…Assume that q ∈ (a) is in  and 𝜙 ∈ Φ p [h, q 𝜐 ] for a given 𝜐 ∈ (0, 1), where q 𝜐 (z) = q(𝜐z) satisfies the conditions in (25). Then, (26) leads to a +  p,𝜅,𝜎,𝜍 𝜇,𝛿,𝜁 𝑓 (z) ≺ q(z) for all z ∈ D. We summarize the relationship between a differential subordination's best dominant and the solution of such a differential equation in a theorem. Theorem 2.6.…”

“…Our interest stems from the fact that the third-order differential subordination theory, introduced by Antonino and Miller 25 for the study of third-order differential subordinations, has turned out to be more involved in the progress of univalent function theory. In other studies, [26][27][28] the authors investigated several third-order differential subordinations results for an operator associated with generalized Struve, generalized Mittag-Leffler, and Hurwitz-Lerch Zeta functions. We should pay special attention to the fact that in Miller and Mocanu, 20 the sharp subordination (i.e., the best dominants for some subordinations) is the univalent solution of some differential equations.…”

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))…”

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

“…In the same year, Ibrahim et al [25] established some third-order differential subordination outcomes for holomorphic functions associated with a fractional integral operator (Carlson-Shaffer operator type). Subsequently, the problems of the third-order differential subordination were studied by El-Ashwah and Hassan [26], El-Ashwah and Hassan [27], Attiya et al ([28,29]), Srivastava et al [30] and Gochhayat and Prajapati [31]. Many of the studies have not yet been investigated utilizing third-order differential subordination technique.…”