We give some results of various kinds concerning Î»-spirallike functions of complex order and Î»-Robertson functions of complex order in the unit disc U = {z : |z| < 1}. They represent extensions and generalizations of many previous results. We mainly used the subordination method.

Let H denote the class of functions f(z) = z+âˆ‘âˆžk=2akzk which are analytic in the unit disc âˆ† = {z : |z| < 1}. In this paper, we introduce the class MÎ» Î±[A,B] of functions f âˆˆ H with f(z)f â€²(z)/z â‰ 0, satisfying for z âˆˆ âˆ† : {(eiÎ» âˆ’Î±cosÎ»)(zf â€²(z)/f(z))+Î±cosÎ»(1+ zf â€²â€²(z)/f â€²(z))} â‰º cosÎ»((1+Az)/(1+Bz))+isinÎ», where â‰º denotes subordination, Î± and Î» are realâ€¦ (More)

A complex valued function f = u+ iv defined in a domain D âŠ‚ C, is harmonic in D, if u and v are real harmonic. Such functions can be represented as f(z) = h(z) + g(z), where h an g are analytic in D. In this paper we study some convolution properties preserved by the integral operator In H,Î»f, n âˆˆ N0 = N âˆª {0}, Î» > 0, where the functions f are univalentâ€¦ (More)