A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="normal">q</mi><mi>̧</mi></mrow></semantics></math></inline-formula>-Calculus

Abstract

Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. The class is proved to be not empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on |α2| and |α3| coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation.

Keywords

• analytic functions
• convolution
• fractional derivatives
• bi-univalent functions
• starlike class
• q ̧ -calculus%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm83333"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="normal">q</mml:mi> <mml:mi>̧</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>-calculus