Related papers: On two new means of two arguments III
In this paper we introduce the concepts of p-logarithmic and Alpha-power divergence measures and point out a number of basic results.
We obtain new inequalities with alternating signs of H\"{o}lder and Minkowski type.
In this paper, we describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
In the paper, the authors find the best possible constants appeared in two inequalities for bounding the Seiffert mean by the linear combinations of the arithmetic, centroidal, and contra-harmonic means.
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
The purpose of this paper is to extend the definition of quasiarithmetic means by taking a strictly monotone generating function instead of a strictly monotone and continuous one. We establish the properties of such means and compare them…
The aim of this paper is to obtain new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. These inequalities give us the possibility to derive estimates from below of the first…
We consider Gini means with short biographical information and propose a new proof of the main inequality for these means. Also some applications of Gini and other means are considered to polymer chemistry.
In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities…
We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics…
Suppose that $X,Y$ are positive random variable and $m$ a numerical (commutative) mean. We prove that the inequality ${\rm E} (m(X,Y)) \leq m({\rm E} (X), {\rm E} (Y))$ holds if and only if the mean is generated by a concave function. With…
We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.
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 obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections…
In this paper, we prove that the double inequality $M_{p}(a,b)<B(a,b)<M_{q}(a,b)% holds for all $a, b>0$ with $a\neq b$ if and only if $p\leq 4\log 2/(4+2\log 2-\pi)=1.2351\cdots$ and $q\geq 4/3$, where $%…
In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.
In this paper, the new weighted inequalities were derived by-distance which is similar to the given inequality for the potential operator defined in [1].
We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in $\R^d$, $d \geq 2$. In particular, we derive upper bounds on Riesz means of order $\sigma \geq 3/2$, that improve the sharp Berezin inequality…