On Oblique Domains of Janowski Function

TL;DR

This paper explores properties of oblique domains related to Janowski functions, providing bounds and extending known results on argument, radius, and subordination for complex parameters.

Contribution

It introduces new bounds for oblique Janowski domains and extends existing results on argument, radius, and subordination to complex parameters.

Findings

Derived bounds for oblique Janowski domains

Extended argument and radius results for complex parameters

Enhanced subordination results involving Janowski functions

Abstract

We investigate certain properties of tilted (oblique) domains, associated with the Janowski function $(1+Az)/(1+Bz),$ where $A,B\in\mathbb{C}$ with $A\neq B$ and $|B|\leq 1$. We find several bounds for these oblique domains. Further, we extend the various known argument, radius, and subordination results involving Janowski functions with complex parameters.