Analyzing convex univalent functions on semi-infinite strip domains

In this paper, a new class of analytic functions called convex univalent functions is introduced. These functions are of the form 1 + 1/alpha log 1 - bz/ 1 -z for a > 0,-1 < b < 1, and they map the open unit disk onto a horizontal semi-infinite strip domain. The paper focuses on function families for which zf'/f maps the unit disk to a subset of this strip domain. Several properties of this class of functions are discussed, including coefficient estimates, extreme points, and growth properties. The paper also explores connections to other classes of functions, such as starlike functions. There are several applications of this class of functions. They can be used in conformal mapping problems and problems related to the analysis of complex networks. The results presented in the paper can also be applied in constructing mathematical models that describe various physical phenomena, such as fluid dynamics and electromagnetism.