Some relations between certain classes of analytic functions

TL;DR

This paper introduces two new subclasses of multivalent analytic functions, explores their relationships through parameter-specific cases, and discusses various implications of these connections.

Contribution

The paper defines two novel subclasses of multivalent functions and investigates their interrelations and consequences based on parameter choices.

Findings

Established connections between the subclasses for specific parameter values

Derived several consequences and properties of the introduced classes

Enhanced understanding of multivalent function subclasses

Abstract

In the present paper we introduce and studied two subclasses of multivalent functions denoted by $\mathcal{M}^{\lambda}_{p,n}(\gamma;\beta)$ and $\mathcal{N}^{\lambda}_{p,n}(\mu,\eta;\delta)$. Further, by giving specific values of the parameters of our main results, we will find some connection between these two classes, and moreover, several consequences of main results are also discussed.