In the paper, a new class of Bazilevič harmonic functions is introduced. First, the sufficient and necessary conditions and integral expressions of the class are proved by the subordination relationship and the basic theory of harmonic functions. Then, the inclusion relation and radius problems are explored, yielding intriguing new findings.

In this paper, we introduce a new class of generalized close-to-convex functions, which are defined by quasi-subordination relationship. The integral expression, the estimation of the first two terms and the Fekete-Szegö problem of functions belonging to the class are obtained. Our results extend and unify previous work on starlike, convex, and close-to-convex functions under quasi-subordination. Examples are provided to demonstrate sharpness.

In this paper, we introduce and study a class of generalized harmonic functions related to the Bazilevič function. We establish necessary and sufficient coefficient conditions, growth estimates, and convex combination properties for this class. Several new results are obtained, extending known properties from analytic to harmonic mappings.