In this paper we present some shorter proofs for Abbas et al.'s results in ℒ-fuzzy normed space, which is not a trivial generalization of fuzzy normed space.
Our study provided some empirical proofs for the AJCC T staging.
The footage shows Williams digging in his bathrobe pockets, apparently looking, unsuccessfully, for some proof of identity.
Wheeler was upset about Liu's report that Wheeler's PAC pulled an ad after a local TV station asked for some proof of the ad's claims.
In general, results show a higher percentage of fMRI tasks were completed in groups that received the multiple reward compliance protocol, providing some proof of concept data for the approach.
Mesopotamian, Indian and Chinese mathematicians are all known to have discovered the theorem independently and, in some cases, provide proofs for special cases.
In Section 3, we review some existing results and offer simpler proofs for some of them.
New (direct) proofs for some criteria are provided.
In the Appendix, the detailed proofs for some Lemmas and Theorems are given.
The result enables one to obtain elegant proofs for some related inequalities.
