Sentence examples for spaces was obtained from inspiring English sources

The first result for contractive mappings in ordered G-metric spaces was obtained by Saadati et al. [13].

Notice that a similar result for semilinear equations in Hilbert spaces was obtained by Dauer and Mahmudov [27].

Thus in [3], a proof of the generalized Hyers-Ulam stability for the linear mapping between Banach spaces was obtained.

Results for nonseparable spaces are obtained by separable reduction arguments.

As a first application, characterizations of compact uniformly definitizable operators on Pontrjagin spaces are obtained.

Using classic assumptions on the geometry, continuous embeddings between Sobolev and Hölder function spaces are obtained.

Similar results for arbitrary Banach spaces are obtained in both the real-analytic and the Cp settings.

Also a new asymptotic lower bound for projection constants of symmetric spaces is obtained (see Theorem 5.3).

The setting conditions for air-conditioned spaces were obtained as indoor air temperature of 24 28 °C and relatively humidity of 50 70%.

Therefore, the singular condition equation of the input parameters and the singular loci of the input parameters in the basic configuration spaces are obtained.

Refinements in Hilbert spaces and extensions to Banach spaces were obtained by Xu [16].