Sentence examples for by replacing the unbounded from inspiring English sources

Ageneralization of the Rassias theorem was obtained by Gǎvruta [5] by replacing the unbounded Cauchy difference by a general controlfunction.

M. Rassias theorem was obtained by Găvruţa [7] by replacing the unbounded Cauchy difference by a general control function in the spirit of Th.

M. Rassias theorem was obtained by Găvruţa [5] by replacing the unbounded Cauchy difference by a general control function in the spirit of the Th.

A generalization of Rassias' theorem was obtained by Gǎvruta [5] by replacing the unbounded Cauchy difference by a general control function in the spirit of Rassias' approach.

A generalization of the Rassias theorem was obtained by Găvruta [12] by replacing the unbounded Cauchy difference by a general control function in the spirit of Rassias' approach.

M. Rassias theorem was obtained by G vruta [17] by replacing the unbounded Cauchy difference by a general control function in the spirit of Th.M. Rassias' approach.

We study the Hamilton-Jacobi equation of a system governed either by a "semilinear" or by a "monotone" dynamics, replacing the unbounded terms of this equation by their Yosida approximations.

In particular, Rassias [11, 12] proved a similar stability theorem in which he replaced the unbounded Cauchy difference by this factor ||x|| p ||y|| q for p,q ∈ R with p + q ≠ 1.

This work sets the basis for further studies beyond the spatially periodic case studied in [15], where the hypothesis of spatial periodicity allows one to replace the unbounded (hyperbolic) domain by a compact one, hence making the functional analysis much simpler.

A new type of stability for functional equations was introduced by Aoki [6] and Rassias [7] by replacing (varepsilon ) in the Hyers theorem with a function depending on (x) and (y), such that the Cauchy difference can be unbounded.

M. Rassias [4] for the unbounded Cauchy difference proved a similar stability theorem in which he replaced the factor by for with (see also [22] for a number of other new results).  .