Sentence examples for be the subclass of 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)|<∞.

Let S be the subclass of A consisting of univalent functions [1].

Let S be the subclass of A consisting of univalent functions in U with the normalized condition f ( 0 ) = 0 = f ′ ( 0 ) − 1.

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.

Let H(U) be the class of functions analytic in U = { z ∈ ℂ : | z | < 1 } and H[a, n] be the subclass of H(U) consisting of functions of the form f z) = a + a n z n + a n +1zn+1 +..., with H0 = H[0, 1] and H = H[1, 1].

Let (mathcal{A}_{n}) ((ninmathbb{N})) be the class of certain analytic functions (f z)) in the open unit disk (mathbb{U}) and (mathcal{P}_{n}(lambda)) be the subclass of (mathcal{A}_{n}) consisting of (f z)) which satisfy (|f"(z)| leqq lambda) ((lambda> 0)) in (mathbb{U}).

Let S, K, S ∗, and C be the subclasses of A which consist of univalent, close-to-convex, starlike (with respect to origin), and convex functions, respectively.

Let Σ ∗ and Σ k be the subclasses of Σ 1 consisting of all functions which are, respectively, meromorphically starlike and meromorphically convex in D (see, for details, [1, 5]).

Let S ∗ and K be the subclasses of A ( n ) consisting of all starlike functions f ( z ) in U and of all convex functions f ( z ) in U, respectively.

and R ≡ R is the subclass of consisting of prestarlike functions of order α which was introduced by Suffridge [10].

One type of generalized Hampel filter that was not discussed in connection with the simulation example was the subclass of cascade interconnections of Hampel filters and/or recursive Hampel filters.