Sentence examples for by using this notion from inspiring English sources

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By using this notion, we generalize some fixed point theorems presented by Minak and Altun [7], Kamran [26] and those contained therein.

Thereafter, many researchers improved and generalized fixed point results by using this notion for single valued and multi-valued mappings (cf. e.g. [3, 7, 20] for details).

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We further refined this by using the notion of gene coherence; in doing so we discovered that a number of genes are strongly incoherent, behaving erratically across the studies.

In this paper, by using the notion of asymptotic log-likehood and the martingale convergence theorem, and extending the analytic technique proposed by Liu [9], Liu and Yang [7] to the case of discrete-time and continuous-state nonhomogeneous Markov chains, we obtain the strong deviation theorem for discrete-time and continuous-state nonhomogeneous Markov chains.

In this paper, by using the notion of a fuzzy soft set together with arithmetic operations on fuzzy number, we apply the fuzzy soft set technology through well-known Sanchez's [8] approach for medical diagnosis, and we exhibit the technique with a hypothetical case study.

MB-OPLS was designed to overcome this problem by using the notion that OPLS also can be used for normalization purposes [ 33].

In this paper, we generalize the result of Boyanov and Veselinov by using the notion of σ-convergence.

Boyanov and Veselinov [3] have proved the Korovkin theorem on C [ 0, ∞ ) by using the test functions 1, e − x, e − 2 x. In this paper, we generalize the result of Boyanov and Veselinov by using the notion of statistical summability ( C, 1 ) and the same test functions 1, e − x, e − 2 x.

In this paper, an iterative sequence for relatively nonexpansive multi-valued mappings by using the notion of generalized projection is introduced, and then weak and strong convergence theorems are proved.

By using the notion of a "second-order" function a function that takes other functions as arguments—Frege was able to give such an account.

A non-cumulative version of the realist view of progress can be formulated by using the notion of truthlikeness.

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