Let denote the class of normalised analytic functions defined by for .
For the authors introduce the class of normalised analytic -logarithmically convex functions defined in the open unit disc by
For , a best possible subordination theorem is obtained which implies that forms a subset of the starlike functions . Some extreme coefficient problems are also solved.
This definition and some properties are inspired by the well known -convex functions, introduced in 1969 by P. T. Mocanu. The principal proofs of this paper are based on the so called “admissible functions method” defined and developed by P. T. Mocanu and S. S. Miller, method which used differential subordinations.