2023-06-04T05:20:56Z
https://jims.ims.ir/?_action=export&rf=summon&issue=16199
Journal of the Iranian Mathematical Society
JIMS
2021
2
1
Sanov's theorem on Lie relators in groups of exponent $p$
M.
Vaughan-Lee
I give a proof of Sanov's theorem that the Lie relators of weight at most $2p-2$ in groups of exponent $p$ are consequences of the identity $px=0$ and the $(p-1)$-Engel identity. This implies that the order of the class $2p-2$ quotient of the Burnside group $B(m,p)$ is the same as the order of the class $2p-2$ quotient of the free $m$ generator $(p-1)$-Engel Lie algebra over GF$(p)$. To make the proof self-contained I have also included a derivation of Hausdorff's formulation of the Baker Campbell Hausdorff formula.
Sanov's theorem
Lie relators
Groups of exponent $p$
2021
01
01
1
16
https://jims.ims.ir/article_110856_87c80830a05958c113d30d5f05f1c835.pdf
Journal of the Iranian Mathematical Society
JIMS
2021
2
1
Generalized trapezoid type inequalities for functions with values in Banach spaces
S.
Dragomir
Let E be a complex Banach space. In this paper we show among others that, if α:[a,b]→C is continuous and Y:[a,b]→E is strongly differentiable on the interval (a,b), then for all u∈[a,b],‖(∫_{u}^{b}α(s)ds)Y(b)+(∫_{a}^{u}α(s)ds)Y(a)-∫_{a}^{b}α(t)Y(t)dt‖ ≤{┊max{∫_{u}^{b}|α(s)|ds,∫_{a}^{u}|α(s)|ds}∫_{a}^{b}‖Y′(t)‖dt, [∫_{u}^{b}(b-t)|α(t)|dt+∫_{a}^{u}(t-a)|α(t)|dt]sup_{t∈[a,b]}‖Y′(t)‖, ≤(b-a)^{1/p}[(∫_{u}^{b}|α(s)|ds)^{p}+(∫_{a}^{u}|α(s)|ds)^{p}]^{1/p} ×(∫_{a}^{b}‖Y′(t)‖^{q}dt)^{1/q}for p, q>1 with (1/p)+(1/q)=1. Applications for operator monotone functions with examples for power and logarithmic functions are also given.
Banach spaces
integral inequalities
Operator monotone functions
2021
01
01
17
38
https://jims.ims.ir/article_138341_5a034622d668c9097177e956cd4e849e.pdf
Journal of the Iranian Mathematical Society
JIMS
2021
2
1
On a Hilbert-type integral inequality in the whole plane
M.
Rassias
B.
Yang
G.
Meletiou
Using weight functions and techniques of real analysis, a new Hilbert-type integral inequality in the whole plane with nonhomogeneous kernel and a best possible constant factor is proved. Equivalent forms, several particular inequalities and operator expressions are considered.
Hilbert-type integral inequality
weight function
parameter
equivalent form
operator
2021
01
01
39
51
https://jims.ims.ir/article_141199_a726440e0929ea956c8fa65786aab4ca.pdf
Journal of the Iranian Mathematical Society
JIMS
2021
2
1
The first eigenvalue of $\left(p,q\right)$-elliptic quasilinear system along the Ricci flow
S.
Azami
M.
Habibi Vosta Kolaei
In this paper we investigate the monotonicity of the first eigenvalue of $\left(p,q\right)$-elliptic quasilinear systems along the Ricci flow in both normalized and unnormalized conditions. In particular, we study the eigenvalue problem for this system in the case of Bianchi classes for $3$-homogeneous manifolds.
Ricci flow
$(p
q)$-elliptic quasilinear system
Eigenvalue
2021
01
01
53
70
https://jims.ims.ir/article_141490_c8292bfa33955943da919d35e5f22c90.pdf