On Generalizations of Hölder's and Minkowski's Inequalities
Mathematical Sciences and Applications E-Notes, cilt.11, sa.4, ss.213-225, 2023 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 4
- Basım Tarihi: 2023
- Doi Numarası: 10.36753/mathenot.1150375
- Dergi Adı: Mathematical Sciences and Applications E-Notes
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.213-225
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Atatürk Üniversitesi Adresli: Evet
Özet
We present the generalizations of Hölder's inequality and Minkowski's inequality along with the generalizations of Aczel's, Popoviciu's, Lyapunov's and Bellman's inequalities. Some applications for the metric spaces, normed spaces, Banach spaces, sequence spaces and integral inequalities are further specified. It is shown that $({mathbb{R}}^n,d)$ and $left(l_p,d_{m,p}right)$ are complete metric spaces and $({mathbb{R}}^n,{left|xright|}_m)$ and $left(l_p,{left|xright|}_{m,p}right)$ are $frac{1}{m}-$Banach spaces. Also, it is deduced that $left(b^{r,s}_{p,1},{left|xright|}_{r,s,m}right)$ is a $frac{1}{m}-$normed space.