Sentence examples for both discrete and integral from inspiring English sources

In both discrete and integral cases, the point c belongs to the convex hull of the set (mathcal{S}), as the smallest convex set containing (mathcal{S}).

Improvements are related to the discrete and integral part of the inequality.

Now we obtain generalizations of discrete and integral Jensen-type linear functionals with real weights.

Very general forms of discrete and integral quasi-arithmetic means and their refinements were studied in [6].

The inequality (1.1) may be classified into several types (discrete and integral etc)., which is of great importance in analysis and its applications [1, 2].

The intention of this paper is still more to connect the quoted implication (in the extended form) with convex functions, in the discrete and integral case.

Using the way of weight functions and the techniques of discrete and integral Hilbert-type inequalities with some additional conditions on the kernel, a half-discrete Hilbert-type inequality with a general homogeneous kernel of degree − λ ∈ R and a best constant factor k ( λ 1 ) is obtained as follows: ∫ 0 ∞ f ( x ) ∑ n = 1 ∞ k λ ( x, n ) a n d x < k ( λ 1 ) ∥ f ∥ p, ϕ ∥ a ∥ q, ψ (6).

The inequality (1.1) may be classified into several types (discrete and integral etc)., being the following integral form: If f, g are real functions such that 0 < ∫ 0 ∞ f 2 ( x ) d x < ∞, 0 < ∫ 0 ∞ g 2 ( x ) d x < ∞, then we have [1] ∫ 0 ∞ ∫ 0 ∞ f ( x ) g ( y ) x + y d x d y < π ∫ 0 ∞ f 2 ( x ) d x ∫ 0 ∞ g 2 ( x ) d x 1 2, (1.2).

Both discrete delays and continuous delays with integral form are considered here.

The most well known of these operators that have been promoted in the world of fractional calculus are the Riemann Liouville, Caputo (continuous and discrete fractional differential and integral operators), and Grunwald Letnikov (discrete fractional differential operator) (see [1]).

When the group (G) is discrete and countable, the integral over (G) reduces to a sum.