Third Order Differential Subordination for Analytic Functions Involving Convolution Operator

Abstract

In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

$K^{th}$-order Differential Subordination Results of Analytic Functions in the Complex Plane

“…They extended the theory of second-order differential subordination in U introduced by Miller and Mocanu [10] to the third-order case that satisfy the third-order differential subordination {ψ(p(z), zp (z), z 2 p (z), z 3 p (z); z) : z ∈ U } ⊂ Ω. Recently, the several authors have considered the applications of these results to third-order differential subordination for analytic functions in U for example (see [1,3,4,7,8,13,[15][16][17]). In 2020, Atshan et al [2] extended the theory of third-order differential subordination in U introduced by Antonino and Miller [1] to the fourth-order case.…”

Third-Order Differential Subordination for Generalized Struve Function Associated with Meromorphic Functions

“…A univalent dominant ꝗ satisfying ꝗ ≺ Ҩ for all dominants of Eq 1 is referred to as the best dominant . 4,5 Let ∑(𝑝, 𝒾) be the class of all meromorphic functions of the form:…”

Results of Third-Order Strong Differential Subordinations

“…The Sȃlȃgean differential operator was employed for introducing a new class of analytic functions in [9], and the Ruscheweyh differential operator in [10] for defining a new class of univalent functions and for studying strong differential subordinations. The Sȃlȃgean and Ruscheweyh operators were used together in the study presented in [11], and a multiplier transformation provided new strong differential subordinations in [12][13][14]. The Komatu integral operator was applied for obtaining new strong differential subordinations results [15,16], and other differential operators proved effective for studying strong differential subordinations [17].…”