In this paper we prove among others that
where
is an analytic function on the domain D, x, y,
with
are the resolvent functions for the elements y and x, and γ is a closed rectifiable path in D and ...such that
Applications for the exponential function on the Banach algebra
are also given.
Let
$ r_e(\mathbf {S}) $
r
e
(
S
)
be the Euclidean spectral radius associated with a q-tuple
$ \mathbf {S}=(S_1,\ldots,S_q) $
S
=
(
S
1
,
...
,
S
q
)
of bounded linear operators on a complex Hilbert ...space. The principal objective of our study is to establish various compelling upper bounds involving
$ r_e(\cdot ) $
r
e
(
⋅
)
. In particular, our findings demonstrate that, for all
$ t\in \left 0,1\right $
t
∈
0
,
1
, we have
\ r_{e}\left( \mathbf{S}\right) \leq \frac{1}{2}\max \left\{ \omega(\mathbf{S}),\omega \left( \Delta _{t}(\mathbf{S})\right) \right\} +\frac{1}{2}\left\Vert \mathbf{S}\right\Vert ^{\frac{1}{2}}\left\Vert \mathbf{S}\right\Vert_{e}^{\frac{1}{2}}. \
r
e
(
S
)
≤
1
2
max
{
ω
(
S
)
,
ω
(
Δ
t
(
S
)
)
}
+
1
2
||
S
||
1
2
||
S
||
e
1
2
.
Here,
$ \Delta _{t}(\mathbf {S}) $
Δ
t
(
S
)
represents the generalized spherical Aluthge transform of
$ \mathbf {S} $
S
, while the notations
$ \omega (\cdot ) $
ω
(
⋅
)
,
$ \|\cdot \| $
||
⋅
||
, and
$ \|\cdot \|_e $
||
⋅
||
e
pertain to the joint numerical radius, joint operator norm, and Euclidean operator norm, respectively, of operators in Hilbert spaces. Furthermore, we extend the notions of spherical and Duggal transforms and derive multiple upper bounds for
$ r_{e}\left ( \mathbf {S}\right ) $
r
e
(
S
)
in relation to these transforms. Additionally, there are some applications that are derived as well.
In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.
In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means ...of two positive real numbers and give the error estimations for the trapezoidal formula.
In this study, the assumption of being differentiable for the convex function f in the (p, q)-Hermite-Hadamard inequality is removed. A new identity for the right-hand part of (p, q)-Hermite-Hadamard ...inequality is proved. By using established identity, some (p, q)-trapezoid integral inequalities for convex and quasi-convex functions are obtained. The presented results in this work extend some results from the earlier research.
In this paper, we establish some Hermite‐Hadamard type inequalities for the Generalized Riemann‐Liouville fractional integrals
Ia+,gαf and
Ib−,gαf, where g is a strictly increasing function on
a,b, ...having a continuous derivative on
a,b and under the assumption that the composite function f∘g−1 is h ‐convex on
ga,gb. Some applications for Hadamard fractional integrals and s‐Godunova‐Levin type convex functions are also provided.
We establish in this paper some Jensen’s type inequalities for functions defined by power series with
nonnegative coefficients. Applications for functions of selfadjoint operators on complex Hilbert ...spaces are provided
as well.
Refinement of the Jensen integral inequality Sever Dragomir, Silvestru; Adil Khan, Muhammad; Abathun, Addisalem
Open mathematics (Warsaw, Poland),
1/2016, Letnik:
14, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
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