Sentence examples for proved the corresponding from inspiring English sources

Meanwhile, they proved the corresponding fixed point theorems.

As their special cases, they proved the corresponding inequalities involving Riemann-Liouville and Erdélyi-Kober type fractional integral operators.

As a characterization of H p n p ( R n ), Edmunds and Triebel [3] proved the corresponding Hardy-type inequality with a logarithmic correction as follows.

Alber and Guerre-Delabrere [1] introduced the concept of weak contractions in Hilbert spaces and proved the corresponding fixed point result.

Specially, Li and Liu [4] stated and proved the corresponding boundedness and compactness characterizations for C φ from H ∞ (U n ) to B log α ( U n ).

Very recently, Gu et al.[18] motivated and inspired by the results of Marino and Xu [15], Yao et al.[17] introduced and studied two iterative schemes for solving hierarchicalvariational inequality problem and proved the corresponding strong convergenceresults for the generated sequences in the context of a countable family ofnonexpansive mappings under suitable conditions on parameters.

We also develop weak topologies for this theory and prove the corresponding compactness and convergence results.

We then show the correctness of this specification by proving the corresponding probability distribution properties within the HOL theorem prover, summarizing the proof steps.

In this paper, we discuss the developable surface which contains a given 3D Bézier curve as geodesic and prove the corresponding conclusions in detail.

For, we can construct the graph as in case, and prove the corresponding results accordingly.

Now we prove the corresponding estimates for (mathcal{I}_{Omega,alpha }) hold.