Sentence examples for the subclass of functions from inspiring English sources

Let N1 denote the class of generalized Nevanlinna functions with one negative square and let N1, 0 be the subclass of functions Q z)∈N1 with the additional properties limy→∞ Q iy)/y=0 and lim supy→∞ y |Im Q iy)|<∞.

Finally, denote by the subclass of functions in where.

(i) For β = 0, we have the subclass of Bazilevic functions defined by Patel [12].

For β = 0, we have the subclass of Bazilevic functions defined by Patel [12].

For β = 0, p = 1, g ( z ) = z, A = 1 − 2 ρ, B = − 1, we obtain the subclass of Bazilevic functions defined in [13].

(ii) For β = 0, p = 1, g ( z ) = z, A = 1 − 2 ρ, B = − 1, we obtain the subclass of Bazilevic functions defined in [13].  .

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).

Let S be the subclass of A consisting of functions f z) which are univalent in U. A function f ( z ) ∈ S is said to be starlike with respect to the origin in U if f U is the starlike domain.

By S, it is denoted the subclass of the univalent functions in A and by S* and K--the subclasses of S whose members are starlike (with respect to the origin) and convex in U, respectively.

In the paper, we consider the classes of functions which generalize these subclasses of functions.

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