相关论文: A generalized mean value inequality for subharmoni…
We investigate functions with the property that for every interval, the slope at the midpoint of the interval is the same as the average slope. More generally, we find functions whose average slopes over intervals are given by the slope at…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
In this article we extend the mean value property for harmonic functions to the nonharmonic case. In order to get the value of the function at the center of a sphere one should integrate a certain Laplace operator power series over the…
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.
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
We show that p-harmonic functions in the plane satisfy a nonlinear asymptotic mean value property for p>1. This extends previous results of Manfredi and Lindqvist for certain range of p's.
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
Motivated by the mean value property of harmonic functions, we introduce the local and global median value properties for continuous functions of two variables. We show that the Dirichlet problem associated with the local median value…
The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.
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…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
We prove a generalization of the fact that periodic functions converge weakly to the mean value as the oscillation increases. Some convergence questions connected to locally periodic nonlinear boundary value problems are also considered.
This paper deals with more refinements of inequalities related to deviations from Mean Value involving superquadratic and uniformly convex functions.
Weighted mean value identities over balls are considered for harmonic functions and their derivatives. Logarithmic and other weights are involved in these identities for functions. Some applications of weighted identities are presented.…
Famous Redheffer's inequality is generalized to a class of anti-periodic functions. We apply the novel inequality to the generalized trigonometric functions and establish several Redheffer-type inequalities for these functions.
We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic functions and essentially almost subharmonic…
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.
In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.
We obtain several inequalities on the generalized means of dependent p-values. In particular, the weighted harmonic mean of p-values is strictly sub-uniform under several dependence assumptions of p-values, including independence, negative…
In this work, a generalization of Chebyshev functional is presented. New inequalities of Gruss type via Pompeiu's mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Gruss inequality…