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

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 14
• Main Authors: Khan, Bilal, Srivastava, H. M., Arjika, Sama, Khan, Shahid, Khan, Nazar, Ahmad, Qazi Zahoor
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 06.06.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Analytic functions; Calculus; Convolution; Derivatives; Difference and Functional Equations; Differential subordination; Functional Analysis; Hadamard product (or convolution); Mathematical analysis; Mathematics; Mathematics and Statistics; Multivalent (or p-valent) functions; Operators (mathematics); Ordinary Differential Equations; Partial Differential Equations; q-Analogue of Ruscheweyh’s derivative operator; q-Derivative (or q-Difference) operator; 30C45; Analytic functions; 30C50; valent) functions; 11B65; Differential subordination; Analogue of Ruscheweyh’s derivative operator; Derivative (or; 47B38; Hadamard product (or convolution); 30C80; Multivalent (or; Difference) operator
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03441-6

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.