Convolution Results with Subclasses of <i>p</i>-Valent Meromorphic Function Connected with <named-content content-type="inline-formula"><inline-formula><math display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula></named-content>-Difference Operator

Abstract

Applying the operator of q-difference, we examine the convolution properties of the subclasses MSζ,qr,p(A,B) and MKζ,qr,p(A,B) of p-valent meromorphic functions defined in the punctured open-unit disc. We derived specific inclusion features and coefficient estimates for functions that fall into these subclasses. Additionally, connections between the results presented here and those discovered in earlier papers are emphasized.

Keywords

• q -derivative operator%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm100000"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-derivative operator
• analytic functions
• starlikeness
• convolution
• differential subordination
• q -analogue multiplier operator%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm1001"> <mml:semantics> <mml:mi mathvariant="fraktur">q</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-analogue multiplier operator