Bi-Starlike Function of Complex Order Involving Rabotnov Function Associated With Telephone Numbers

Sa’ud Al-Sa’di, Kaliappan Vijaya and Gangadharan Murugusundaramoorthy

Journal of Mathematics, 2025, vol. 2025, 1-18

Abstract: Telephone numbers defined through the recurrence relation Qn=Qn−1+n−1Qn−2 for n≥2, with initial values of Q0=Q1=1. The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi-convex and bi-starlike functions of complex order in the open unit disk by utilizing the normalized Rabotnov function and defining a new linear operator subordinated with generalized telephone numbers. We also obtain bounds of the initial Taylor–Maclaurin coefficients, a2 and a3, for these functions and determine the Fekete–Szegö inequalities. In addition, several related corollaries are presented. These findings are based on the recent study of the Rabotnov function and demonstrate its significance in the field.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1256437

DOI: 10.1155/jom/1256437

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