TY  - JOUR
TI  - On Generalizations of Hölder's and Minkowski's Inequalities
AB  - 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.
AU  - SELAMET, UĞUR
DO  - 10.36753/mathenot.1150375
PY  - 2023
JO  - Mathematical Sciences and Applications E-Notes
VL  - 11
IS  - 4
SN  - 2147-6268
SP  - 213
EP  - 225
DB  - TRDizin
UR  - http://search/yayin/detay/1211163
ER  -