Sentence examples for consisting of function from inspiring English sources

One of the largest classes of univalent functions is the class of strongly starlike functions of order α, (0consisting of function (fin mathcal{A}) such that bigglvert arg biggl[frac{zf' z)}{f z)} biggr] biggrvert < frac{alphapi}{2} quad (zinmathbb{D}).

Moreover, assume that the embedding is compact; then the set consisting of functions, such that (2.20).

Let be the corresponding class consisting of functions such that lies in the region.

Let ({mathcal{A}}) denote the subclass of ℋ consisting of functions normalized by (f(0)=0), (f'(0)=1).

Let denote the subclass of ℋ consisting of functions normalized by f ( 0 ) = 0 and f ′ ( 0 ) = 1.

We denote by K the subclass of A consisting of functions which are convex of order α in U (see, [1, 2]).

For any function if then is a simple zero of if For any integer and any define sets consisting of functions satisfying the following conditions: (i).

Let be the subspace of consisting of functions "vanishing at infinity," and be the space of bounded regular Borel measure on with the variation norm.

Also let, S ∗ and K denote the subclasses of consisting of functions which are univalent, starlike of order γ and convex of order γ in, respectively.

Finally, in terms of a differential operator defined by (1.3) above, let denote the subclass of consisting of functions which satisfy the following inequality: (1.5).

From (3.4) and Remark 2.4, we find that the set Q is the family consisting of functions equicontinuous on compact intervals of R +.