Third-Order Differential Inequalities in the Complex Plane

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

“…Next, numerous important studies were presented by ). In 1992, Ponnusamy and Juneja [18] considered the third-order inequalities and subordination. After that, in 2000, Miller and Mocano in their monograph [19] provided a marvelous and extensive discussion on this theory with numerous implementations.…”

Third-Order Differential Subordination and Differential Superordination Results for Analytic Functions Involving the Srivastava-Attiya Operator

“…Though the notion of third order differential subordination have originally found in the work of Ponnusamy and Juneja [13]. The recent work due to Tang et al [18,20] on third order differential subordination attracted to many researchers in this field.…”

“…The recent work due to Tang et al [18,20] on third order differential subordination attracted to many researchers in this field. For example see [4,8,9,14,18,19,20,13,11]. In the present paper we considered suitable classes of admissible functions associated with Srivastava-Attiya operator and obtained sufficient conditions on the normalized analytic function f such that Sandwich-type subordination of the following form holds:…”

Third Order Differential Subordination of Analytic Function Defined by Fractional Derivative Operator

“…The theory of first and second order differential subordination has been used by many authors to solve problems in this field. There are few articles dealing with third order inequalities and subordination (see [1] and [6]). Jeyaraman et al [4] have also applied the third order subordination result on Schwarzian derivative.…”