By using functions of bounded variation we generalize the class of strongly starlike functions and related classes. The main object is to obtain characterizations and inclusion properties of these classes of functions.

Some subclasses of analytic functions f(z) in the open unit disk U are introduced. In the present paper, Some interesting sufficient conditions, including coefficient inequalities related close-to-convex functions f(z) of order α with respect to a fixed starlike function g(z) and strongly starlike functions f(z) of order μ in U, are discussed. Several special cases and consequences of these coe...

*Correspondence: [email protected] 1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia Full list of author information is available at the end of the article Abstract The estimates for the second Hankel determinant a2a4 – a3 of the analytic function f (z) = z + a2z + a3z + · · · , for which either zf ′(z)/f (z) or 1 + zf ′′(z)/f ′(z) is subordinate to a certai...