An Application of Sălăgean Operator Concerning Starlike Functions

Abstract

As an application of the well-known Sălăgean differential operator, a new operator is introduced and, using this, a new class of functions Sn(α) is defined, which has the classes of starlike and convex functions of order α as special cases. Original results related to the newly defined class are obtained using the renowned Jack–Miller–Mocanu lemma. A relevant example is given regarding the applications of a new proven result concerning interesting properties of class Sn(α).

Keywords

• analytic function
• starlike function of order α
• convex function of order α
• Sălăgean differential operator
• Alexander integral operator