Differential subordination associated with generalised derivative operator

The authors have recently introduced a new generalised derivatives operator ¿_¿1,¿2 ^n,m, which generalised many well-known operators studied earlier by many different authors. The trend of finding new operators such as the differential or the integral operators has attracted many researchers and in fact, has become necessary to some of the researchers. The aim of this paper is to use the equality relation (1 + n)¿_¿1,¿2 ^n+1,m f(z) = z(¿_¿1,¿2 ^n,m f(z))´ + n(¿_¿1,¿2 ^n,m f(z)), to discuss some interesting results using the technique of differential subordination. The results include the subordination and the inclusion. Whenever n = 0, ¿₂ = 0 we have results given by Oros.