Sentence examples for spaces existence from inspiring English sources

Using an analytic framework of a suitable family of products of fractional Sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates.

Our results allow us to present a unified approach to characterising completeness of spectral metric spaces, existence of connections on modules, self-adjointness and regularity of induced operators on tensor product C⁎-modules and the lifting of Kasparov products to the unbounded category.

As applications of contractive mapping theorem on complete C ∗ -algebra-valued mexistenceces, existence and uniqueness results for a type of integral equation and operator equation are given.

Notice also that in ordered abstract spaces, existence of some fixed point theorems is presented and applied the resolution of matrix equations (see, e.g., [10 12]).

As applications of contractive mapping theorem on complete (C^{ast } -algebra-valued b-metric spaces, existence and uniqueness results for a type of operator equation and integral equation are given.

In 2008, Rus [20] investigated the basic problems of metric fixed point theory in the case of partial metric spaces: existence and uniqueness, the convergence of successive approximations and well posedness of the fixed point problem.

Alireza Razavi and his firm Studio Razavi Architects are participating in the exhibition Time – Space – Existence, organized by the European Cultural Center and Global Art Affairs Foundation at the Palazzo Bembo, Palazzo Mora, and Palazzo Rossini, San Marco.

Then there are Guastavino spaces whose existence is almost a matter of archaeological interest.

In reflexive Banach spaces, the existence of weak solutions or pseudo-solutions for fractional differential equations were studied in [32 36].

Their idea was to obtain, in β-normed spaces, the existence of the exact solution and the error estimations by using the fixed point alternative theorem [6].

By introducing a new kind of weak solutions, which are based on the weighted variable exponent Sobolev spaces, the existence and stability of the weak solutions are proved in this paper.