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).

New Developments in Geometric Function Theory

“…In another study [2], Hatun Özlem Güney, Georgia Irina Oros, and Shigeyoshi Owa provide an application of the well-known Sălăgean differential operator for defining a new operator, through which a new class of functions is defined, which has the classes of starlike and convex functions of order α as special cases. The renowned Jack-Miller-Mocanu lemma is applied for obtaining interesting properties for the newly defined class of functions.…”

Properties of a Special Holomorphic Function Linked with a Generalized Multiplier Transformation

“…The Ruscheweyh differential operator [4] and the Sȃlȃgean differential operator [5] are frequently used by researhers in their findings. Interested readers can refer to [6] for an application of the Sȃlȃgean operator. These operators have been generalized in GFT by adding new ones.…”

Certain Subclasses of Analytic and Bi-Univalent Functions Governed by the Gegenbauer Polynomials Linked with q-Derivative

“…Jackson was the first one to work on the application of q-calculus (see [1][2][3][4]). Recently, incorporating the q-derivative operator into the criterion of differential subordination, many researchers have introduced new subclasses of analytic functions and investigated their geometric properties (see [5][6][7][8][9][10][11][12][13][14][15]). In addition, q-calculus has been widely applied in various realistic systems such as viscoelastic models, neural network models and so on [16][17][18][19][20][21].…”