Sentence examples for function or f from inspiring English sources

Click Insert, then Function (or f on the task bar) to open Insert Function window.

Suppose that f n ⇒ χ f in Δ ′ ( z 0, r ), where f is a nonconstant meromorphic function or f ≡ ∞ in Δ ′ ( z 0, r ).

We say that f : I → R is an h-convex function or that f belongs to the class S X ( I ), if f is non-negative and f ( α x + ( 1 − α ) y ) ≤ h f ( x ) + h ( 1 − α ) f ( y ). for all x, y ∈ I and α ∈ ( 0, 1 ).

We say that f : I → R is a Godunova-Levin function or that f belongs to the class Q ( I ) if f is nonnegative, and for all x, y ∈ I and t ∈ ( 0, 1 ), we have f ( t x + ( 1 − t ) y ) ≤ f ( x ) t + f ( y ) 1 − t. (1.2).

We say that f : I → R is a ( p, h ) -convex function or that f belongs to the class g h x ( h, p, I ), if f is non-negative and f ( [ α x p + ( 1 − α ) y p ] 1 p ) ≤ h f ( x ) + h ( 1 − α ) f ( y ) (2.1).

Definition 2 Let h : J → R be a non-negative function, h ≢ 0. We say that f : I → R is an h-convex function, or that f belongs to the class S X ( h, I ), if f is non-negative and for all x, y ∈ I, α ∈ ( 0, 1 ], we have f ( α x + ( 1 − α ) y ) ≤ h f ( x ) + h ( 1 − α ) f ( y ).

Let h : J → R be a nonnegative function, h ≢ 0. We say that f : I ⊆ R → R is an h-convex function, or that f belongs to the class S X ( h, I ), if f is nonnegative, and for all x, y ∈ I and t ∈ [ 0, 1 ], we have f ( t x + ( 1 − t ) y ) ≤ h ( t ) f ( x ) + h ( 1 − t ) f ( y ).

[6] We say that (f Irightarrow mathbb {R} ) is a Godunova Levin function or that f belongs to class Q(I) if f is non-negative and for all (x,yin I) and (tin (0,1)) we have begin{aligned} f(tx+ 1-t y)le frac{1}{tx+ 1-t yac{1}{1-t}f(y).

The problem is to find a target function (or model) (f :mathbb{R }^qrightarrow mathbb{R }) so that (f(mathbf{x}_k)=y_k), (k=1, 2,ldots,M) or at least, (f(mathbf{x}_k)approx y_k), (k=1, 2,dots,M).

We say that f : [ 0, b ] → R is an ( h, m ) -convex function, or say, f belongs to the class SMX ( ( h, m ), [ 0, b ] ), if f is nonnegative and, for all x, y ∈ [ 0, b ] and t ∈ [ 0, 1 ] and for some m ∈ ( 0, 1 ], we have f ( t x + m ( 1 − t ) y ) ≤ h ( t ) f ( x ) + m h ( 1 − t ) f ( y ).

A function f : I → ℝ is called an h-convex function, or that f belongs to the class SX h, I), if for all x, y ∈ I and t ∈ (0, 1) we have f ( t x + ( 1 - t ) y ) ≤ h ( t ) f ( x ) + h ( 1 - t ) f ( y ).