New criteria for meromorphic $p$-valent starlike functions

Let B,Xa) be the class of functions of the form /(*)=--/-+ 2 akzk (a_p*0, /><=JV={1, 2, ・■・}) which are regular in the punctured disc £/*= {z : 0< \z\<1} and satisfying -j ^ fT § ~{p+l)}<~~a {n(EN≫={0> X> ■■■}'izl<1' °^a<P)> where D≫f(z)= azp + S(/>+m)≫am_12Bl-1 m =\ It is proved that Bn+1(a)cBn(a). Since B0(a) is the class of meromorphically />-valentstarlike functions of order a, all functions in Bn(a) are jb-valent starlike. Further a property preserving integrals is considered.