Abstract
In the present paper, using Jack's lemma, the authors investigate the differential in- equality (1 − α) Ip(n,λ)f(z) zp + α Ip(n+1,λ)f(z) Ip(n,λ)f (z) − 1 < μ, z ∈ E regarding multivalent functions defined by multiplier transfomation in the open unit disk E = {z : |z| < 1}. As consequences, sufficient conditions for univalence, starlikeness and strongly starlikeness of certain analytic functions are obtained.
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