Univalent functions with positive coefficients involving Touchard polynomials

TL;DR

This paper explores relationships among subclasses of univalent functions with positive coefficients in the unit disk, using convolution operators involving Touchard polynomials to establish new connections.

Contribution

It introduces novel convolution operators with Touchard polynomials to connect different subclasses of univalent functions with positive coefficients.

Findings

Established new connections between subclasses of univalent functions

Applied Touchard polynomial-based convolution operators

Enhanced understanding of analytic univalent functions with positive coefficients

Abstract

The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Touchard polynomials. To be more precise, we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk U.