Sentence examples for without completeness from inspiring English sources

In this paper, using the concept of a w-distance on a metric space, we first prove the existence of a fixed point theorem for generalized w α -contraction multivalued mappings without completeness in metric spaces.

In this section, we present sharpened forms of Theorems 1-4, which are new results on their own and are proved without completeness (of the metric space), without continuity (of the underlying mapping) and without the ICU property/DCL property/MCB property (of an ordered metric space).

(f) Let us finally mention that properties of Definitions 3.1-3.3 3.1-3.3orems 4.1 and 4.2 concerning 'righTheoremsomitted in our presentation; we may provide them by constructing appropriate examples (without assuming that T is continuous, without completeness of spaces in a usual sense and without separability of spaces) and applying analogous technique as above.

Oversimplifying and without completeness, given the variety of approaches present in literature, one can distinguish two main classes of clustering approaches.

Without aiming completeness, and without going into any details, we refer to Stacy and Mihram (1965), Harter (1967), Rahman and Gokhale (1996), Varanasi and Aazhang (1989), Do and Vetterli (1988), Mineo and Ruggieri (2005), González-Farías et al. (2009), Saatci and Akan (2010).

Without claiming completeness, we mention some of them.

Without the completeness of these data, it can be established that the hormones or molecules which can bind to the hormone receptors, provoke imprinting in the perinatal period, which resulted in alterations of many physiological processes.

The completeness of data within each of those databases is also unclear; investigators might have excluded those without complete exposure and outcome data from analyses.

The industry should propose technology allowing SR without compromising accuracy, completeness, workflows, and cost-benefit balance.

In the following remark, we obtain the same conclusion without normality and completeness assumptions.

Thus, these optimizations can be generalized to any policy without losing the completeness of the planning search.