In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so-called radical convex functions and study ...their properties. We will see that such convex functions are bounded above by new curves, rather than straight lines. Applications including discrete and continuous Jensen inequalities, subadditivity behavior, Hermite–Hadamard and integral inequalities will be presented.
Ando-Hiai and Golden-Thompson inequalities Sababheh, Mohammad; Moradi, Hamid Reza
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas,
2022/1, Letnik:
116, Številka:
1
Journal Article
Recenzirano
Our main target in this article is to present complementary inequalities of Golden-Thompson and Ando-Hiai types. For example, under mild conditions on the positive definite matrices
A
,
B
, we show ...the complementary Golden-Thompson inequality
e
pA
σ
v
e
pB
1
p
≤
θ
1
p
e
A
∇
v
B
,
0
≤
v
≤
1
,
for any matrix mean
σ
v
between the weighted harmonic mean
!
v
and the weighted arithmetic mean
∇
v
, where
‖
·
‖
is an arbitrary unitarily invariant norm and
θ
being a constant depending on
p
>
1
and
v
. Further inequalities of Golden-Thompson and Ando-Hiai types will be presented for the domain
v
∉
0
,
1
and for means other than the geometric mean.
We prove an inner product inequality for Hilbert space operators. This inequality will be utilized to present a general numerical radius inequality using convex functions. Applications of the new ...results include obtaining new forms that generalize and extend some well known results in the literature, with an application to the newly defined generalized numerical radius. We emphasize that the approach followed in this article is different from the approaches used in the literature to obtain such versions.
From positive to accretive matrices Bedrani, Yassine; Kittaneh, Fuad; Sababheh, Mohammad
Positivity,
09/2021, Letnik:
25, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The main goal of this paper is to discuss the recent advancements of matrix means from positive matrices to accretive matrices in a more general setting. In particular, we present the general form ...governing the well established definition of geometric mean, then we define arbitrary matrix means and functional calculus for accretive matrices. Applications of this new discussion involve generalizations of known inequalities from the setting of positive matrices to that of accretive matrices. This includes the arithmetic-harmonic mean comparisons, monotonicity of matrix means, Ando’s inequality, Choi’s inequality, Ando–Zhan subadditive inequality and much more.
In this paper, we develop a concept of a logarithmically superquadratic function. Such a class of functions is defined via superquadratic functions. We first establish some new properties of ...superquadratic functions. In particular, we derive the corresponding superadditivity relation and its reverse, as well as the external form of the Jensen inequality and its reverse. Then, as a direct consequence of the established results, we obtain the corresponding properties for logarithmically superquadratic functions. Further, we show that logarithmically superquadratic functions with values greater than or equal to one are convex and logarithmically superadditive. In particular, we also obtain the corresponding refinement of the Jensen inequality in a product form. Finally, we give a variant of the Jensen operator inequality for logarithmically superquadratic functions.
This paper presents some inner product inequalities for Hilbert space operators having closed ranges. The obtained results are applied to obtain new bounds for the numerical radius and the operator ...norm, where the Moore-Penrose inverse plays a keen role.
A simple convex approach and block techniques are used to obtain new sharpened versions of numerical radius inequalities for Hilbert space operators. These include comparisons of norms of operators, ...their Cartesian parts, their numerical radii, and the numerical radius of the product of two operators.
In this paper, we present refinements of Kato’s inequality; then, we employ these refinements to obtain some norm and numerical radius inequalities. Our results improve some celebrated inequalities ...in the literature.
Further Inequalities for Convex Functions Sababheh, Mohammad; Moradi, Hamid Reza; Gümüş, Ibrahim Halil
Bulletin of the Malaysian Mathematical Sciences Society,
2023/1, Letnik:
46, Številka:
1
Journal Article
Recenzirano
The main goal of this paper is to present some new properties of convex functions, including Mercer-type, superadditive-type, and Jensen-type inequalities. Applications of these new properties will ...cover the celebrated Hermite–Hadamard inequality, Clarkson inequality, and the operator Mercer inequality. Comparisons with some existing results will be discussed too.
This paper uses matrix monotone functions as a key tool to obtain several relations among the singular values of certain celebrated matrix quantities. This includes, but is not limited to, relations ...among the blocks of a block matrix, relations about the singular values of the matrix Heinz means, and some related matrix combinations. Our results improve some celebrated results from the literature.
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