Related papers: On the Isomorphic Means and Comparison Inequalitie…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms…
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
In recent papers the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the the…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
Using the results of \cite{P1}, we get some estimates of warping functions for isometric immersions by changing the target manifolds by some types of Riemannian manifolds: constant space forms and Hermitian symmetric spaces. And we deal…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
In the present paper, we introduced the extended bicomplex plane $\bar{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about the convergence of the sequences of…
An equidistant set in the Euclidean space consists of points having equal distances to both members of a given pair of sets, called focal sets. Having no effective formulas to compute the distance of a point and a set, it is hard to…
Meaning can be generated when information is related at a systemic level. Such a system can be an observer, but also a discourse, for example, operationalized as a set of documents. The measurement of semantics as similarity in patterns…
The paper presents a new and simple range characterization for the spherical mean transform of functions supported in the unit ball in even dimensions. It complements the previous work of the same authors, where they solved an analogous…
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider H\"older-,…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…