Sentence examples for of functions order from inspiring English sources

In this case, we write S α − lim f k ( x ) = f ( x ) on A. S α − lim f k ( x ) = f ( x ) means that for every δ > 0 and 0 < α ≤ 1, there is an integer N such that 1 n α | { k ≤ n : | f k ( x ) − f ( x ) | ≥ ε  for every  x ∈ A } | < δ. for all n > N ( = N ( ε, δ, x ) ) and for each ε > 0. The set of all pointwise statistically convergent sequences of functions order α will be denoted by S α ( f ).

On 1 July 1999, The National Assembly for Wales (Transfer of Functions) Order 1999 came into effect, this transferred all powers from the Secretary of State for Wales to the National Assembly for Wales, responsibility for the construction of the debating chamber transferred at the same time.

CUDA provides the cudaEvent family of functions in order to measure process time in a GPU.

A mobile peer has a simplified set of functions in order to fit in mobile systems.

The set of all strongly p-Cesàro summable sequences of functions of order α will be denoted by w p α ( f ).

The well-known result that the classes of starlike functions of order and convex functions of order are closed under convolution with prestarlike functions of order follows from the following.

For,, and are, respectively, the familiar classes of starlike functions of order and consisting of convex functions of order.

are the classes of starlike functions of order and convex functions of order in, respectively.

More generally, for, the classes of convex functions of order and starlike functions of order are, respectively, defined by or.

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

Let denote the class of starlike functions of order.