Logarithmic Coefficient Bound for Special Subclasses of Analytic Functions

Samra Shaheen; Saima Mustafa

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Logarithmic Coefficient Bound for Special Subclasses of Analytic Functions

Author(s)

Samra Shaheen Rawalpindi Women University, Rawalpindi, Pakistan.

Saima Mustafa Rawalpindi Women University, Rawalpindi, Pakistan.

Abstract

The study extends the classical theory of Bazilevic functions by introducing ageneralized class incorporating both growth and rotational distortion parameters. We establish sharp bounds for logarithmic coefficients and Taylor series coefficients, revealing how the interaction between these parameters control function behavior. Our main results provide a unified framework that recovers known special cases while generating new insights for the extended class. The analysis combines techniques from geometric function theory with innovative applications of integral mean estimates and coefficient bounds. Key findings demonstrate the optimality of these bounds through comparison with extremal functions and highlight the delicate balance between growth and rotation in coefficient estimation. This work not only advances the theoretical understanding of Bazilevic-type functions but also provides tools for further investigations in complex analysis. The results open several research directions,including optimization of bounding constants and exploration of geometric properties in this broader functional space.

Publication Details

Page(s) 154-154

DOI DOI not available

Published Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025

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Keywords

convex, starlike, and Caratheodory Class., Normalized, Bazilevic, Univalent, Analytic

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