Sentence examples for corollary concern from inspiring English sources

Their troops cared mainly about social issues, but many had a corollary concern about tax relief for their families.

From Theorem 3.1, we obtain the following corollary concerning the stability of (1.5) in the sense of the JMRassias stability of functional equations controlled by the mixed product-sum of powers of norms introduced by J. M. Rassias [26] and called JMRassias stability by several authors [27 30].

Tending s to zero we infer that N ( Q ( x ) - f ( x ), t ) ≥ N ′ ( φ q ( 0, x ), ( k 2 - α ) t ). for all x ∈ X and all t > 0. From Theorem 3.2, we obtain the following corollary concerning the generalized Hyers-Ulam stability [4] of quadratic mappings satisfying (1.5), in normed spaces.

As applications, one has the following corollaries concerning the stability of (1.6).

Hence, by Theorem 2.1, we get the following corollaries concerning the Hyers-Ulam-Rassias stability.

Interestingly, in view of relation (1.4), we arrive at the following corollaries concerning Saigo fractional integral operator.

Besides being an application to those results, it provides interesting corollaries concerning special functions, regions and curves.

In both cases, the rooted product G was considered without any restrictions on graphs G and Γ. Herein, we present a new general result and its corollaries concerning the case when the core graph G is restricted to be bipartite.

We remark that the expressions from Theorem 3.3 and Corollary 3.1 concern the expansion of Euler's constant in terms of the Riemann zeta function evaluated at positive odd integers.

Our next corollary is concerned with weak ϕ contractions.

The claim of Corollary C.4 concerning (H rtimes mathbf{Z }) applies to the group (mathrm{Alt}_f(mathbf{Z }) rtimes _{mathrm{shift}} mathbf{Z }).