Related papers: Around Jensen's inequality for strongly convex fun…

In this paper we achieve some new Hadamard type inequalities using elementary well known inequalities for functions whose first derivatives absolute values are s-geometrically and geometrically convex. And also we get some applications for…

In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…

We define in the space of n by m matrices of rank n, n less or equal than m, the condition Riemannian structure as follows: For a given matrix A the tangent space of A is equipped with the Hermitian inner product obtained by multiplying the…

In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other…

This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the…

We prove that if $u:\mathbb{R}^n\to\mathbb{R}$ is strongly convex, then for every $\varepsilon>0$ there is a strongly convex function $v\in C^2(\mathbb{R}^n)$ such that $|\{u\neq v\}|<\varepsilon$ and $\Vert u-v\Vert_\infty<\varepsilon$.

Several unitarily invariant norm inequalities and numerical radius inequalities for Hilbert space operators are studied. We investigate some necessary and sufficient conditions for the parallelism of two bounded operators. For a finite rank…

This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…

In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities…

In this paper, we introduce the notion of strongly {\varphi}-convex functions with respect to c>0 and present some properties and representation of such functions. We obtain a characterization of inner product spaces involving the notion of…

There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasing functions. Leveraging this distinction, we introduce…

In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of…

First the Hardy and Rellich inequalities are defined for the submarkovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are sufficient to deduce the Rellich inequality from the Hardy…

In this paper the Jessen's type inequality for normalized positive $C_0$-semigroups is obtained. An adjoint of Jessen's type inequality has also been derived for the corresponding adjoint-semigroup, which does not give the analogous results…

We give simple new proofs of two well-known results for the Schr\"odinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity of the first Dirichlet eigenfunction. Our proof of the first…

Let $\mathscr{M}$ be a finite von Neumann algebra with a faithful normal tracial state $\tau$ and $\mathfrak{A}$ be a finite subdiagonal subalgebra of $\mathscr{M}$ with respect to a $\tau$-preserving faithful normal conditional expectation…

In [B1, Theorem 2.36] we proved the equivalence of six conditions on a continuous function f on an interval. These conditions define a subset of the set of operator convex functions, whose elements are called strongly operator convex. Two…

In this study, the author establish some inequalities of Hadamard like based on convex and s-convexity in the second sense. Some applications to special means of positive real numbers are also given.

In this paper, strongly $(\alpha,T)$-convex functions, i.e., functions $f:D\to \R$ satisfying the functional inequality $$ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)-t\alpha\big((1-t)(x-y)\big)-(1-t)\alpha\big(t(y-x)\big)$$ for $x,y\in D$ and $t\in…

Several new improvements of the $A$-numerical radius inequalities for operators acting on a semi-Hilbert space, i.e., a space generated by a positive operator $A$, are proved. In particular, among other inequalities, we show that…