Janowski type close-to-convex functions associated with conic regions

Area of Science:

• Complex Analysis
• Geometric Function Theory

Background:

• Analytic functions mapping the unit disk to specific regions are crucial in geometric function theory.
• Previous work by Noor and Malik introduced petal and oval type regions.

Purpose of the Study:

• To define and investigate analytic functions associated with Noor and Malik's petal and oval regions.
• To explore geometric properties of these newly defined close-to-convex functions.

Main Methods:

• Utilizing concepts from geometric function theory.
• Analyzing properties of analytic functions and their associated close-to-convex functions.
• Investigating geometric characteristics such as coefficient estimates and arc length.

Main Results:

• Defined new classes of analytic functions associated with petal and oval regions.
• Established sufficiency criteria for these functions.
• Determined coefficient estimates and analyzed arc length and growth rates.
• Investigated integral preserving properties.

Conclusions:

• The study successfully defined and characterized new analytic functions.
• The geometric properties investigated provide insights into the behavior of these functions.
• These findings contribute to the understanding of close-to-convex functions in geometric function theory.