Convolution Properties of Meromorphic <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script" mathsize="80%">P</mi></mrow></semantics></math></inline-formula>-Valent Functions with Coefficients of Alternating Type Defined Using <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">q</mi></mrow></semantics></math></inline-formula>-Difference Operator

Abstract

Certain characteristics of univalent functions with negative coefficients of the form f(z)=z−∑n=1∞a2nz2n,a2n>0 have been studied by Silverman and Berman. Pokley, Patil and Shrigan have discovered some insights into the Hadamard product of P-valent functions with negative coefficients. S. M. Khairnar and Meena More have obtained coefficient limits and convolution results for univalent functions lacking a alternating type coefficient. In this paper, using the q-Difference operator, we developed the a subclass of meromorphically P-valent functions with alternating coefficients. Additionally, we obtained multivalent function convolution results and coefficient limits.

Keywords

• meromorphic functions
• alternating series
• q-calculus
• analytic functions
• P -valent%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula> <mml:math id="mm15131"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script" mathsize="80%">P</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>-valent
• starlike function