Sentence examples for abstract integral from inspiring English sources

We illustrate how this "vector-valued harmonic conjugation" result generalizes the various abstract successors of the M. Riesz theorem and we introduce an application to the superdiagonalization of kernels for abstract integral operators.

The solution is studied as a fixed point of the abstract integral equation.

Pierri [9] discussed the existence of S-asymptotically and asymptotically ω-periodic solutions to an abstract integral equation.

In Section 3, we reduce the existence of delay KdV-type equation (1.1) to the local existence of mild solution of abstract integral equation.

In order to investigate minimal sufficient conditions for an abstract integral to belong to the convex hull of the integrand, we propose a system of axioms under which it happens.

Consider the following abstract integral equation: int_{0}^{infty}kappa ttau odot U tau), mathrm{d} tau=psi(t),quad x>0 with a real-valued function (kappa(t)) and a given fuzzy-valued function (psi(t)).

For generalizations to abstract Lebesgue integral; see [7 9].

It turns out to be useful to study Bihari type inequalities with abstract Lebesgue integral.

However, the sharpness of the constant 1 2, a generalization for the abstract Lebesgue integral, and the discrete version of it have been obtained in [7].

The integrals are understood as the abstract Kurzweil-Stieltjes integral and the studied equations are usually called generalized linear differential equations (in the sense of Kurzweil, cf. (Kurzweil in Czechoslov. Math. J. 7 82):4195749, 1957) or (Kurzweil in Generalized Ordinary Differential Equations: Not Absolutely Continuous Solutions, 2012)).

Basic theory of the abstract Kurzweil-Stieltjes integral (called also abstract Perron-Stieltjes or simply gauge-Stieltjes integral) and generalized linear differential equations in a general Banach space has been established by Schwabik in a series of papers [8 10] written between 1996 and 2000.