On Third-Order Differential Subordination and Superordination Properties of Analytic Functions Defined by a Generalized Operator

Abstract

In this current study, we aim to give some results for third-order differential subordination and superordination for analytic functions in involving the generalized operator . The results are derived by investigating relevant classes of admissible functions. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted. The properties and results of the differential subordination are symmetry to the properties of the differential superordination to form the sandwich theorems.

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

“…Certain classes of admissible functions are described and particular uses of third-order differential subordination for p-valent functions associated with generalized fractional differintegral operator are examined in [17] using the third-order differential subordination fundamental results. Using the same idea of defining suitable classes of admissible functions generates interesting results involving a generalized operator in [18] and concerning special functions in [19,20].…”

New Results on Higher-Order Differential Subordination and Superordination for Univalent Analytic Functions Using a New Operator

“…(ν), ν 3 superordination and the principle of third-order differential subordination. For examples of asymmetrical subordination and superordination on a third-order case, see ( [3,4,[30][31][32][33][34][35][36][37][38][39]). Antonino and Miller [4] presented basic concepts and expanded Miller and Mocanu's [1] principle of second-order differential subordination in the open unit disk to the third-order case.…”

On Some Sandwich Results of Univalent Functions Related by Differential Operator

“…Using the results (see [11,[18][19][20][21][22][23][24][25][26][27][28][29][30][31]) t𝑜 o𝑏𝑡ain suffici𝑒nt co𝑛𝑑itions for normalized an𝑎lytic functi𝑜ns to s𝑎𝑡isfy:…”