Related papers: On Some Integral Means
Several mean value identities for harmonic and panharmonic functions are reviewed along with the corresponding inverse properties. The latter characterize balls, annuli and strips analytically via these functions.
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1<p<=2, and to operators under a trace for arbitrary p>1. Applications to trace functions are…
In 1973, E.J. McShane proposed an alternative definition of the Lebesgue integral based on Riemann sums, where gauges are used decide what tagged partitions are allowed. Such an approach does not require any preliminary knowledge of Measure…
The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…
We shall give a refinement of the arithmetic-geometric mean inequality.
We study mean value properties of harmonic functions in metric measure spaces. The metric measure spaces we consider have a doubling measure and support a (1,1)- Poincar\'e inequality. The notion of harmonicity is based on the Dirichlet…
Let $\mathcal{H}ol(B_d)$ denote the space of holomorphic functions on the unit ball $B_d$ of $\mathbb{C}^d$, $d\ge 1$. Given a log-convex strictly positive weight $w(r)$ on $[0,1)$, we construct a function $f\in\mathcal{H}ol(B_d)$ such that…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1<p<\infty$, following the scheme described in Manfredi et al. (2009) for the Euclidean case. The new tool that allows us…
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…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
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…
This paper investigates the existence, nonexistence, and qualitative properties of p-harmonic functions in the upper half-space $\mathbb{R}^N_+ \, (N \geq 3)$ satisfying nonlinear boundary conditions for $1<p<N$. Moreover, the symmetry of…
This article introduces Huber means on Riemannian manifolds, providing a robust alternative to the Frechet mean by integrating elements of both square and absolute loss functions. The Huber means are designed to be highly resistant to…
We prove the Harnack inequality for antisymmetric $s$-harmonic functions, and more generally for solutions of fractional equations with zero-th order terms, in a general domain. This may be used in conjunction with the method of moving…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…