Related papers: A note on the Neuman-S\'andor Mean
We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for subharmonic functions. We also obtain integral inequalities…
In this paper, authors generalize logarithmic mean $L$, Neuman-S\'andor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these…
In this paper, we present the best possible parameters $\alpha_i, \beta_i\ (i=1,2,3)$ and $\alpha_4,\beta_4\in(1/2,1)$ such that the double inequalities \begin{align*}…
These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…
We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to…
This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper…
We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented
Maximal estimates for Schr\"odinger means and convergence almost everywhere of sequences of Schr\"odinger means are studied.
An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic functions.
In this note we revisit the classical geometric-arithmetic mean inequality and find a formula for the difference of the arithmetic and the geometric means of given $n\in\mathbb N$ nonnegative numbers $x_1,x_2,\dots,x_n$. The formula yields…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
In this paper, we give the Assouad dimension formula and the upper bound of the lower dimension for homogeneous Moran sets under the condition $\sup_{k\ge 1}\{n_{k}\}<+\infty$. We also give the Assouad spectrum and the lower spectrum…
We give a simple proof of the fact that an "$f$-estimate" for the $\bar\partial$-Neumann problem implies a lower bound on the geomatric type of the boundary along any complex one dimensional variety. The proof uses the existence of peak…
Harmonic, Geometric, Arithmetic, Heronian and Contraharmonic means have been studied by many mathematicians. In 2003, H. Evens studied these means from geometrical point of view and established some of the inequalities between them in using…
This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that…
New upper and lower limits are given for the number of S-wave bound states yielded by an attractive (monotonic) potential in the context of the Schrodinger or Klein-Gordon equation.
We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.
In the context of non-relativistic quantum mechanics, we obtain several upper and lower limits on the mean square radius applicable to systems composed by two-body bound by a central potential. A lower limit on the mean square radius is…