Some Classes of Differential Subordinations and Their Applications

Abstract:

      Let G be univalent in the unit disc Δ. Let φ:C²×Δ→C be analytic in a domain D?C and let p(z) be analytic in Δ with (p(z), zp′(z);z)∈D when z∈Δ . Assume that p(z) satisfies the differential subordination φ(p(z), zp′(z): z)(?)G(z), z∈A ,(where “(?)”denotes subordination). We determine some conditions on φ and G so that Rep(z)>ρ in Δ and give some applications of these resullts .