Inclusion Relations for Dini Functions Involving Certain Conic Domains

Abstract

In recent years, special functions such as Bessel functions have been widely used in many areas of mathematics and physics. We are essentially motivated by the recent development; in our present investigation, we make use of certain conic domains and define a new class of analytic functions associated with the Dini functions. We derive inclusion relationships and certain integral preserving properties. By applying the Bernardi-Libera-Livingston integral operator, we obtain some remarkable applications of our main results. Finally, in the concluding section, we recall the attention of curious readers to studying the q-generalizations of the results presented in this paper. Furthermore, based on the suggested extension, the (p,q)-extension will be a relatively minor and unimportant change, as the new parameter p is redundant.

Keywords

• analytic function
• univalent function
• starlike and convex function
• subordination
• quasi-convex functions
• Bessel functions