Related papers: Mathematical inequalities on some weighted means
In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by…
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…
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…
We prove local inequalities for analytic functions defined on a convex body in $\Re^{n}$ which generalize well-known classical inequalities for polynomials.
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…
We analyze a bead sliding game and relate it to some classical convex inequalities.
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
Classically, Jensen's Inequality asserts that if $X$ is a compact convex set, and $f:K\to \mathbb{R}$ is a convex function, then for any probability measure $\mu$ on $K$, that $f(\text{bar}(\mu))\le \int f\;d\mu$, where $\text{bar}(\mu)$ is…
In this paper we obtain some new refinements and reverses of Young's operator inequality. Extensions for convex functions of operators are also provided.
During the study of the topic of limit summability of functions (introduced by the author in 2001), we encountered some types of functions that are related to the mean value theorem. In this paper, we formally define mean value and…
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.
In this paper, we obtain some new upper bounds for differantiable mappings whose q-th powers are geometrically convex and monotonically decreasing by using the H\"older inequality, Power mean inequality and properties of modulus.
This paper deals with more refinements of inequalities related to deviations from Mean Value involving superquadratic and uniformly convex functions.
In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
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 article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
In this article, we establish weighted strong and weak type inequalities for non-commutative square functions that naturally arise in the analysis of differences between ball averages and martingale sequences within the framework of group…