Related papers: Convex functions and means of matrices

Some new Hermite-Hadamard's inequalities for h-convex functions are proved, generalizing and unifying a number of known results. Some new applications for special Means of real numbers are also derived.

Subaddivity type matrix inequalities for concave funcions and symetric norms are given.

In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two…

In this paper, we extend the Hermite-Hadamard type $\dot{I}$scan inequality to the class of symmetrized harmonic convex functions. The corresponding version for harmonic h-convex functions is also investigated. Furthermore, we establish…

In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They…

It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as…

In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.

Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in \cite{PSMA2016}. As…

In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.

We study the convexity/concavity properties of the generalized $p$-trigonometric functions in the sense of P. Lindqvist with respect to the power means.

In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.

In the present paper we establish some new integral inequalities analogous to the well known Hadamard inequality by using a fairly elementary analysis.

A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.

This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…

In this paper we extend some notions, previously defined for log-concave functions, to the larger domain of so-called {\alpha}-concave functions. We begin with a detailed discussion of support functions - first for log-concave functions,…

In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of $v$, namely $v\in \mathbb{R}$. These modified inequalities are used to establish corresponding operator inequalities on a…

In this paper, we state some characterizations of $h$-convex function is defined on a convex set in a linear space. By doing so, we extend the Jensen-Mercer inequality for $h$-convex function. We will also define $h$-convex function for…

Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…

In this paper, we establish three inequalities for differentiable s-geometrically and geometrically convex functions which are connected with the famous Hermite-Hadamard inequality holding for convex functions. Some applications to special…

Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…