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

[摘要] 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.

[学科分类] 航空航天科学

[关键词] 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