Related papers: Conditional $h$-convexity with applications
We introduce the notion of regular operator mappings of several variables generalising the notion of spectral function. This setting is convenient for studying maps more general than what can be obtained from the functional calculus, and it…
There are given conditions for represention of a function of many arguments as the difference of convex functions.
In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csisz\'{a}r \cite{csi1} $f-$divergence. A result is established that…
We prove inequality (1) for the modified Steiner functional A(M), which extends the notion of the integral of mean curvature for convex surfaces.We also establish an exression for A(M) in terms of an integral over all hyperplanes…
In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.
In this paper, two new lemmas are proved and inequalities are established for co-ordinated convex functions and co-ordinated s-convex functions.
The well known Jensen inequality, holds true for every convex functions. However, we found that it is possible to apply it to some problems related to nonconvex functions for which Jensen's inequality holds true locally. Having considered a…
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
In this paper, we establish Hermite-Hadamard inequality for interval-valued convex function on the co-ordinates on the rectangle from the plane. We also present Hermite-Hadamard inequality for the product of interval-valued convex functions…
In this paper we deduce a formula for the fractional Laplace operator $(-\Delta)^{s}$ on radially symmetric functions useful for some applications. We give a criterion of subharmonicity associated with $(-\Delta)^{s}$, and apply it to a…
In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.
In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.
In this work, several inequalities of Popoviciu type for h-MN-convex functions are proved, where M or N are denote to Arithmetic, Geometric and Harmonic means and $h$ is a non-negative superadditive or subadditive function.
In this paper, we study operator mean inequalities for the weighted arithmetic, geometric and harmonic means. We give a slight modification of Audenaert's result to show the relation between Kwong functions and operator monotone functions.…
In this paper, the notation of strongly log-convex functions with respect to c>0 is introduced and versions of Hermite Hadamard-type inequalities for strongly logarithmic convex functions are established.
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
We obtain operator concavity (convexity) of some functions of two or three variables by using perspectives of regular operator mappings of one or several variables. As an application, we obtain, for $ 0<p < 1,$ concavity, respectively…
Given an nxn doubly stochastic matrix P satisfying an appropriate condition of linear algebraic-type, and a function f defined on a nonempty interval, we show that the validity of a convexity-type functional inequality for f in terms P…
In this paper we investigate continuity properties of functions $f:\mathbb{R}_+\to\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\big(H_p(x,y)\big)\leq H_q(f(x),f(y)) \qquad(x,y>0), $$ where $H_p$ stands for the…
It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…