Sentence examples for which were generalized from inspiring English sources

In the same lieu, Nieto and Rodríguez-López [4] proved some variants of the Ran and Reuring fixed point theorem for increasing mappings, which were generalized by many authors (e.g. [5 16]) in recent years.

On the other hand, in LC-spaces, Wu and Li [6] obtained the approximate selection theorems for quasi-lower semicontinuous multimaps which were generalized by the author and Lee [7] to almost lower semicontinuous multimaps in C-spaces.

NTDO engineering is done in a middle-out approach, as it was started by general classes (taken from universal terms frequently found in table headers and domain database schemas), which were generalized upward to the BioTop connection level, but also specialized downward to the required leaf node level dictated by the envisioned query granularity.

First, we introduce some results of nonnegative tensors [10 12], which are generalized from nonnegative matrices.

The example demonstrates that our main result is an actual improvement over the results which are generalized.

C1 summability which was generalized by various investigators using different summability methods with different sets of conditions.

In this paper, a further family of refinable functions is constructed, which includes pseudo-splines of Type II, based on refinement masks, which are generalized Bernstein polynomials.

The shape factor of every sample was calculated using Eq. 2, which was generalized based on the circularity factor defined by ISO 9276-6 [26].

Harris ([1915]) developed the first inventory model, Economic Order Quantity, which was generalized by Wilson ([1934]) who gave a formula to obtain economic order quantity.

In particular, a very powerful tool is the Banach fixed point theorem, which was generalized and extended in various directions (see [1 37]).

Then they proved a weak convergence theorem which is generalized simultaneously theorems of Browder and Petryshyn [12] and Gol'shteĭn and Tret'yakov [13].