On Generalized Spiral-Like Analytic Functions


Khalida Inayat Noor, Nazar Khan, Muhammad Aslam Noor




In this paper, we use the concept of bounded Mocanu variation to introduce a new class of analytic functions, defined in the open unit disc, which unifies a number of classes previously studied such as those of functions with bounded radius rotation and bounded Mocanu variation. It also generalizes the concept of $\beta$-spiral likeness in some sense. Some interesting properties of this class including inclusion results, arclength problems and a sufficient condition for univalency are studied.