Advancements in Log-P-Analytic Functions: Landau-Type Theorems and Their Refinements

TL;DR

This paper introduces log-p-analytic functions, develops four Landau-type theorems for poly-analytic functions, refines existing results, and presents specialized versions with concrete outcomes.

Contribution

It introduces the concept of log-p-analytic functions and formulates new Landau-type theorems, including refinements and specialized cases, advancing the theory of poly-analytic functions.

Findings

Four Landau-type theorems for poly-analytic functions

Two theorems with exact results

Refinement of Abdulhadi and Hajj's work

Abstract

This work begins by introducing the groundbreaking concept of log-p-analytic functions. Following this introduction, we proceed to delineate four distinct formulations of Landau-type theorems, specifically crafted for the domain of poly-analytic functions. Among these, two theorems are distinguished by their exactitude, and a third theorem offers a refinement to the existing work of Abdulhadi and Hajj. Concluding the paper, we present four specialized versions of Landau-type theorems applicable to a subset of bounded log-p-analytic functions, resulting in the derivation of two precise outcomes.