A class of meromorphic multivalent functions with negative coefficients defined by a differential operator
For 0???? 0 ? ? ? ? , 0<??1 0 < ? ? 1 , 1/(p+1)<??1 1 / ( p + 1 ) < ? ? 1 , m?N0=N?{0} m ? N 0 = N ? { 0 } and p?N p ? N , a new class M ? ? m p + ( ? , ? ) of meromorphic p p -valent functions defined by means of the differential operator D ? ? p m is introduced and systematically studied. Membership in this class is characterized through coefficient estimates. Distortion, radii of starlikeness and convexity of order ? ( 0 ? ? < 1 ) , Hadamard convolution product, an integral operator, convex combinations and neighborhoods are also investigated.
distortion hadamard convolution product integral operator meromorphically multivalent starlikeness meromorphically multivalent convexity neighborhood of a meromorphic function