Related papers: A sharper bound for the Jensen's operator inequali…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
In this note we prove Jensen-type inequality for certain non-convex functions. We apply our idea to prove some inequalities which were suggested at some high-level math olympiades.
The main target of this paper is to discuss operator Hermite--Hadamard inequality for convex functions, without appealing to operator convexity. Several forms of this inequality will be presented and some applications including norm and…
Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…
In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type…
In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting…
In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse H\"older Inequality for $A_{\infty}$ weights. For two given operators $T$ and $S$, we study $L^p(w)$ bounds of…
We give H\"older's inequalities for integral and conditional expectation involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for the operator are established.
We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.
In this paper, sharp results on operator Young's inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young's inequality. Secondly, we give an additive result, which improves a well-known…
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value…
Let $\mathcal{A}$ be a $C^*$-algebra and $\phi:\cA\to L(H)$ be a positive unital map. Then, for a convex function $f:I\to \mathbb{R}$ defined on some open interval and a self-adjoint element $a\in \mathcal{A}$ whose spectrum lies in $I$, we…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
This is a continuation of our previous paper. We consider a certain order-like relation for positive operators on a Hilbert space. This relation is defined by using the Jensen inequality with respect to the square-root function. We show…
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator…