What does this research mean for the field?

Strict bounds for the initial Taylor-Maclaurin coefficients and Fekete-Szegö inequalities can be established for newly defined subclasses of bi-starlike and biconvex functions of complex order that involve the normalized Rabotnov function subordinated to the Lucas Balancing polynomial. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to explore new subclasses of bi-starlike and biconvex functions involving the Rabotnov function and Lucas Balancing polynomial.

May 17, 2026Analele Universităţii "Ovidius" Constanţa. Seria Matematică0 citationsOpen Access

Bi- Starlike function of complex order involving Rabotnov function subordinated to Lucas Balancing polynomial

KVK. VijayaVellore Institute of Technology University GMG. MurugusundaramoorthyVellore Institute of Technology University DBDaniel Breaz1 Decembrie 1918 University

Key Points

The aim is to explore new subclasses of bi-starlike and biconvex functions involving the Rabotnov function and Lucas Balancing polynomial.
Utilized the normalized Rabotnov function and the concept of subordination.
Defined two subclasses of bi-starlike and biconvex functions in the open unit disc.
Established bounds for the initial Taylor-Maclaurin coefficients and Fekete-Szegö inequalities.
Obtained precise bounds for Taylor-Maclaurin coefficients in the defined subclasses.
Determined Fekete-Szegö inequalities for functions in these classes.
Provided several related corollaries supporting the main findings.

Abstract

Abstract Considering the interesting results obtained recently by studying Rabotnov function, in this paper using the normalized Rabotnov function and the concept of subordination related with the Lucas Balancing polynomial, we defined two new subclasses of the bi-starlike and biconvex function of complex order in the open unit disc and obtained bounds of the initial Taylor-Maclaurin coefficients for functions in these classes. Furthermore, we have determined the Fekete-Szegö inequalities for function in the above mentioned classes. Several related corollaries are also presented.

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Cite This Study

Vijaya et al. (Fri,) studied this question.

synapsesocial.com/papers/6a095bdd7880e6d24efe1b7f https://doi.org/https://doi.org/10.2478/auom-2026-0013

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