A class of analytic functions defined by a second order differential inequality and error function

Abstract

In this article, we introduce and investigate a novel class of analytic functions that are defined through a second-order differential inequality in conjunction with the error function, a fundamental mathematical function widely used in various scientific and engineering applications. The proposed class of functions provides a versatile framework for modeling complex phenomena in diverse fields, including mathematics, physics, engineering, and statistics. And we examine coefficient bound, extreme points, convolution, convexity and radii properties of this subclass. In summary, our investigation into this class of analytic functions, defined by a second-order differential inequality and the error function, not onlsy contributes to the mathematical literature but also provides a powerful tool for solving complex problems in science and engineering. The versatility and potential applications of these functions make them a valuable resource for researchers and practitioners seeking innovative solutions to diverse analytical challenges.