Results on Univalent Functions Defined by <i>q</i>-Analogues of Salagean and Ruscheweh Operators

Abstract

In this paper, we define and discuss properties of various classes of analytic univalent functions by using modified q-Sigmoid functions. We make use of an idea of Salagean to introduce the q-analogue of the Salagean differential operator. In addition, we derive families of analytic univalent functions associated with new q-Salagean and q-Ruscheweh differential operators. In addition, we obtain coefficient bounds for the functions in such new subclasses of analytic functions and establish certain growth and distortion theorems. By using the concept of the (q, δ)-neighbourhood, we provide several inclusion symmetric relations for certain (q, δ)-neighbourhoods of analytic univalent functions of negative coefficients. Various q-inequalities are also discussed in more details.

Keywords

• univalent functions
• <i>q</i>-analogues
• Salagean operators
• <i>q</i>-calculus
• Ruscheweh operators