New Study Maps Coefficient Bounds for Analytic Functions in Nephroid Domains

The work, accepted for publication in Frontiers in Applied Mathematics and Statistics, derives coefficient estimates and Fekete–Szego inequalities for a newly defined class of analytic functions, and then connects those results to fractional integral operators and to a probability distribution known as the neutrosophic Poisson distribution.

The paper, titled “Coefficient Estimation in Nephroid Domains and Its Use in Fractional Operators and Neutrosophic Poisson Distribution Series,” was authored by KMKAVIYAPRIYA M and SHOBANADEVI N of Vellore Institute of Technology in Vellore, India. According to the journal’s listing, the article was received on 6 July 2026 and accepted on 17 September 2026, with the final formatted version to be published soon.

The study centers on a class of analytic functions denoted ℳρ, λ(q). For functions in this class, the authors establish the Fekete–Szego inequality together with associated coefficient bounds.

Recent work in the theory of analytic functions, the authors note, has highlighted the relevance of such domains and their relationships to fractional calculus operators. The present study is motivated by those developments and explores both the geometric and analytic properties of functions whose behavior is tied to the nephroid region.

Beyond the coefficient estimates, the paper examines the behavior of the functions ζϕ(ζ) and their inverses for the class ℳρ, λ(q). The study also covers the convolution of functions in the class with normalized analytic functions, a construction used to describe structural characteristics of the class.

A distinctive feature of the work is its use of the Erdelyi–Kober fractional integral operator. The authors employ this operator to build new connections between fractional operators and analytic function theory, which, they state, improves the applicability of the results.

The final contribution extends the framework into probability. The authors obtain specialized Fekete–Szego inequalities for a subclass of functions using the neutrosophic Poisson distribution series. The authors describe this as revealing new insights into fractional and probabilistic extensions of analytic functions.

The article is published open access under the Creative Commons Attribution License (CC BY), and the journal notes that all claims expressed in the article are solely those of the authors and do not necessarily represent those of their affiliated organizations or the publisher.

The work appears in the Statistics and Probability section of Frontiers in Applied Mathematics and Statistics, and its listed keywords include analytic function, convex function, nephroid domain, neutrosophic Poisson distribution, starlike function, and subordination, reflecting the range of classical and modern tools the study draws together.

Subject of Research: Coefficient bounds and Fekete–Szego inequalities for analytic functions in nephroid domains, with connections to fractional operators and the neutrosophic Poisson distribution

Article Title: Coefficient estimation in nephroid domains and its use in fractional operators and neutrosophic Poisson distribution series

Article References: Kaviyapriya, M., & Shobanadevi, N. (2026). Coefficient estimation in nephroid domains and its use in fractional operators and neutrosophic Poisson distribution series. Frontiers in Applied Mathematics and Statistics, 12, Article 1923663. https://doi.org/10.3389/fams.2026.1923663

Image Credits: AI Generated

DOI: 10.3389/fams.2026.1923663

Keywords: analytic functions, nephroid domain, Fekete-Szego inequality, coefficient bounds, fractional calculus, Erdelyi-Kober fractional integral, neutrosophic Poisson distribution, geometric function theory, convolution, subordination, Coefficient, estimation