Sentence examples for assumptions imposed on from inspiring English sources

Compared with Theorem A (see [26], Theorem 1.1]), on one hand, the assumptions imposed on f are much weaker.

They obtained at least one or two positive solutions under some assumptions imposed on the nonlinearity of by applying Krasnoselskii fixed point theorem.

Under the assumptions imposed on Lemma  3.2.

Some additional assumptions imposed on were needed there.

Strong convergence of this method was established under suitable assumptions imposed on the algorithm parameters.

Actually, this assertion seems impossible under their assumptions imposed on { λ n, i } i = 1 N.

By introducing the integral controllers and free weighting matrix scheme, some restricted assumptions imposing on the switched systems are avoided.

Lin and Liu [6] established the L 2 -stability of peakons for Degasperis-Procesi Eq. (4) under certain assumptions imposing on the initial value.

Thus the assumption imposed on (B_{i}) in Theorem 10 is valid.

The basis is a homogenization/averaging scheme using a micro-randomness assumption imposed on a directional higher gradient interaction term.

In 2007, Wang [10] introduced an explicit hybrid iteration method for nonexpansive mappings in Hilbert space; and then Osilike et al. [11] extended Wang's results to arbitrary Banach spaces without the strong monotonicity assumption imposed on the hybrid operator.