Sentence examples for utilizing this theorem we from inspiring English sources

Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings.

The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.

To utilize this theorem for our problem, first we consider the linearization of system (2.1) in the form of FDE with the derivative order in both equations around a given stationary point.

By utilizing the equivalence theorem, we identify classes of 2-parameter nonlinear models for which a D-optimal design is precisely supported on 2 points.

Utilizing this observation and proof of Theorem 3.3, we obtain the following result.

Utilizing Theorem 3.5, we also obtain the following result immediately.

Utilizing Theorem 3.2, we immediately derive the following result.

Thus, utilizing Theorem 3.1, we obtain the following corollary.

Consequently, utilizing Theorem 4.1 we derive the desired result.

Consequently, utilizing Theorem 3.1 we obtain the desired result.

Utilizing Theorem 3.1 we immediately derive the following.