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 $({\mathbb{R}}^n,{\left\|x\right\|}_m)$ and $\left(l_p,{\left\|x\right\|}_{m,p}\right)$ are $\frac{1}{m}-$Banach spaces. Also, it is deduced that $\left(b^{r,s}_{p,1},{\left\|x\right\|}_{r,s,m}\right)$ is a $\frac{1}{m}-$normed space.
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Articles |
Yazarlar | |
Erken Görünüm Tarihi | 8 Ağustos 2023 |
Yayımlanma Tarihi | 25 Ekim 2023 |
Gönderilme Tarihi | 29 Temmuz 2022 |
Kabul Tarihi | 24 Ocak 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 11 Sayı: 4 |
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