Sentence examples for a real generalization of from inspiring English sources

Therefore, Theorem 4 may not be a real generalization of Theorem 1.

A real generalization of Nadler's theorem was presented by Mizoguchi and Takahashi [15] as follows.

The following example shows that Theorem 5 is a real generalization of Theorem 2.

Hence, the notion of 'cone b-metric' is not a real generalization of neither b-metric nor metric.

The following example illustrates Theorem 2.1 and shows that it is a real generalization of Theorem 3.1 in [8].

An example is also established to show that our result is a real generalization of analogous results for metric spaces [1, 9, 10, 18, 20].

Again, the following examples show that the notion of generalized convex contractions of order 2 is a real generalization for the notions of convex contractions of order 2 and ordered convex contractions of order 2, which were provided, respectively, in [1] and [3].

But the following examples show that the notion of generalized convex contractions is a real generalization for the notions of convex contractions and ordered convex contractions which were provided, respectively, in [3] and [1].

Based on the reduced number of errors in the first sessions we can consider that a real generalization process was involved in the recognition of a cow of the same breed.

Hence, the main result of [3] is not a real generalization.

In the present article, we prove the existence of a coincidence point of a mapping and a relation under a contractive condition which is an innovative and real generalization of the Banach contraction theorem.