EXTENSIONS FOR CERTAIN SUBORDINATION RELATIONS

Abstract

For some complex number γ which has a positive real part, a certain subordination relation concerned with the Bernardi integral operator Iγ was proven by D. J. Hallenbeck and St. Ruscheweyh Proc. Amer. Math. Soc. 52 1975 , 191-195 . By considering the analyticity of the functions defined by the Bernardi integral operator Iγ for some non-zero complex number γ with Re γ ≤ 0, an extension for certain subordination relation are discussed.