A certain q-Ruscheweyh type derivative operator and its applications involving multivalent functions

Abstract

Abstract In the present paper, by using the concept of convolution and q-calculus, we define a certain q-derivative (or q-difference) operator for analytic and multivalent (or p-valent) functions. This presumably new q-derivative operator is an extension of the known q-analogue of the Ruscheweyh derivative operator. We also give some interesting applications of this q-derivative operator for multivalent functions by using the method of differential subordination. Relevant connections with a number of earlier works on this subject are also pointed out.

Keywords

• Analytic functions
• Multivalent (or p-valent) functions
• Hadamard product (or convolution)
• q-Derivative (or q-Difference) operator
• q-Analogue of Ruscheweyh’s derivative operator
• Differential subordination