Sentence examples for existing corresponding from inspiring English sources

In this article we study several classes of sum operator equations on ordered Banach spaces and present some new existence and uniqueness results of positive solutions, which extend the existing corresponding results.

The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal.

Therefore, it is shown that the newly obtained results are less conservative and more applicable than the existing corresponding ones.

Recently, in [29], Zhai and Zhang presented a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results.

The other results in [1] and the fixed point theorems in [2, 3] can be derived from the existing corresponding fixed point theorems in the setting of the standard metric space in the literature.

Namely, they showed that, using the Banach-Alaoglu theorem and the Gelfand representation, the basic result of [1 5] can be reduced to the existing corresponding fixed point theorems in the setting of standard metric spaces.

The exception to this was the ΔF metric for the existing technique corresponding to the two water intervals with the lowest water fluoride content.

Question 2. Referring to "dynamic nature" of interactions that can be observed in MD simulations, it would be interesting to analyze Fig.  5 in terms of major states (long-living interactions) existing between corresponding residues.

The prosecutor's office said in a statement: "Documents with medical contents were confiscated that point towards an existing illness and corresponding treatment by doctors.

Rising industrial action may signal the failure of an existing social consensus and corresponding union weakness rather than a resurgence of union strength.

Now, we present a non-trivial example which shows the generality of Corollary 16 over the corresponding existing theorems.