The Geometric Properties Of Some Meromorphic Star-like Functions

Back in the 1980s and 1990s,meromorphic functions which are starlike with respect to symmetric points and related functions have been studied by several authors.In 1985,M.L.Mogra,T.R.Reddy and O.P.Juneja studied meromorphic univalent functions with positive coefficients;In 1991,S.A.Halim studied functions starlike with respect to other pointsIn 1973,Janowski used the Schwarz function to define the subordination relation,and further used the subordination relation to define a series of subclasses of analytic functions.In recent years,scholars also used the subordination to define different function classes and studied the related properties of these new subclasses of functions.In 2014,D.-G.Yang and J.-L.Liu studied certain subclasses of meromoiphically multivalent functions;In 2015,J.-L.Liu and D.-G.Yang studied on functions starlike with respect to k-symmetric points.In 2017,J.-L.Liu,H.M Srivastava and Y.Yuan studied a family of meromoiphically functions which are starlike with respect to k-symmetric points.Some good properties of these functions,such as distortion inequalities,inclusion relation,convolution properties and partial sum,are obtainedMotivated by their work,first,the present paper uses subordination to define two function classes Mp,?(?,A,B)and Rp,k(?,A,B).Then the distortion inequalities,inclusion relation,convolution properties and partial sum and integral transformation of these two function classes are studied.The paper consists of two partsThe first part is introduction and preliminary results.It introduces the basic concepts,lemma and defines two function classes.The second part discusses some properties of function classes Mp,k(?,A,B)and Rp,k(?,A,B),respectively,distortion bounds,inclusion relation,convolution properties,partial sum and integral transforms.