Sentence examples for for given functions from inspiring English sources

In this paper some results about the Hyers-Ulam-Rassias stability for thelinear functional equations in general form and its Pexiderized can beproved for given functions on general domain to a complex Banach spacesunder some suitable conditions.

where (2.2). holds for all and for given functions.

where is defined as in the beginning of Section 2, is strictly increasing odd function satisfying for, satisfies (4.2). for given functions and   satisfying for, and functions and satisfy that.

The neuropsychological approach in patients with brain lesions is of clear value in establishing the necessity of brain areas for given functions.

For given functions ρ (R̄2), f, and g(R1, R2, R̄1, R̄2), it is always possible to find the optimal nanoshell radii, R ¯ 1 opt and R ¯ 2 opt, which ensure that the photothermal therapy is the most efficient under the circumstances.

For given function, we set.

For given function (u_{k}in H_{h}), we have the following inequality on each triangular element (ein S_{h}): vert nabla w_{0} vert le vert nabla u_{k} vert ^{p-1}.

For those given functions, the problem has a unique solution u_{ex} (x,t,s )=e^{-2t-s}sin x. (18).

For convenience, for a given function ξ ∈ L∞[0, T], we denote the essential supremum and infimum of ξ by ξ* and ξ*, respectively.

A method for determining function (mathsf{G}(m,k)) for a given function (mathsf{F}(m,k)) can be found in [17].

The necessary condition for to possess an extremum for a given function is that satisfies the following -Euler-Lagrange equations: (53).