Similarly, we will prove Corollary 3.1 through the following two steps.
Corollary 2.2, through Lemma 3.1(i), leads directly to the subsequent result.
Without introducing auxiliary equation and the existence result of conjugate points as [2, 4], we can prove this corollary directly through the Sobolev inequality (the idea of the proof origins to Brown and Hinton [5, page 5]).
It is worth pointing out that Corollaries 2.9 through 2.11 were obtained by Nakai in [9].
It should be pointed out that Corollaries 2.1 through 2.3 were given by Komori and Shirai in [10].
Further, our theorem has been validated through Corollary 6.3, which is a result of Bor [14].
So, upon replacing,,, respectively, by,,, and then dividing by, in each of the expressions of Theorem 4.1 through Corollary 4.15, we will get the corresponding symmetric identities for Type. .
So, upon replacing,,, respectively, by,,, and then dividing by, in each of the expressions of Theorem 4.1 through Corollary 4.15, we will get the corresponding symmetric identities for Type.
We will only carry through the details for Corollary 3.
Moreover, we prove that the equality of 4-WFRFT space and multi-WFRFT space through the corollary.
