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Generalized classes of uniformly convex functions

Dziok J., Szpila A.

Journal of Mathematics and Applications

2010

Vol. 33

13-26

In this paper we introduce some subclasses of analytic functions with varying argument of coeffcients. These classes are defined in terms of the Hadamard product and generalize the well-known classes of uniformly convex functions. We investigate the coeffcients estimates, distortion properties, radii of starlikeness and convexity for defined classes of functions.

The classes of functions which can be defined by subordination

Jurasińska R., Szpila A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1998

z. 22 [170]

41-49

Let H = H(U) be the class of all functions which are holomorphic in the unit disc U = {z : \z\ < 1}. Let P(n) denotes the class of all functions p(z) = 1+piz+... is an element H, such thatp(pz) -< (1+zn/(1-zn), where -< denotes subordination. With the class P(n) we connect the subclass S*(n) of starlike functions in the following way. A function f(z) = z + a2z + ... belongs to S* (n) if and only if zf'(z)/f(z) is an element of P(n). In this note we give the estimations of some coefficients in the classes P(n) and S*(n) and we find the radius of convexity of the class S*(n).

On some subclass of strongly starlike functions

Jurasińska R., Szpila A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1998

z. 22 [170]

29-39

In this paper for fixed natural number n we define subclass S*/n,(alpha) of strongly starlike functions [...].