Inclusion Relations for Dini Functions Involving Certain Conic Domains

作者：Khan, Bilal; Khan, Shahid; Ro, Jong-Suk^*; Araci, Serkan; Khan, Nazar; Khan, Nasir

来源：Fractal and Fractional, 2022, 6(2): 118.

DOI：10.3390/fractalfract6020118

• analytic function
• univalent function
• starlike and convex function
• subordination
• quasi-convex functions
• Bessel functions
• Dini functions
• Primary 30C45
• 30C50
• 30C80
• Secondary 11B65
• 47B38

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 <mml:semantics>(p,q)</mml:semantics>-extension will be a relatively minor and unimportant change, as the new parameter <mml:semantics>p</mml:semantics> is redundant.