Related papers: Short note on Smithson's paper concerning Arzel\`a…
The purpose of this paper is to develop some methods to study Riesz type inequalities, Hardy-Littlewood type theorems and smooth moduli of holomorphic, pluriharmonic and harmonic functions in high-dimensional cases. Initially, we prove some…
We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which…
We generalize the definition of topological entropy given by Adler, Konheim, and McAndrew (AKM) for piecewise continuous self-maps defined on a compact interval (pc-maps). For this notion of entropy, we prove that the properties of the…
The paper is devoted to the fixed point theory in four aspects: of contractions, nonexpansive mappings, generalized inward mappings, and of the tool theorems. The manuscript was written about ten years ago. At first Nadler's concept of…
In this article, a new class of operators, termed Ad-contractions, is introduced to extend the framework of A-contractions to the setting of dislocated metric spaces. Fixed point results are established for single mappings, sequences of…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…
Polysymmetric functions, introduced by Asvin G and Andrew O'Desky as a generalization of symmetric functions, have natural connections to algebraic geometry and provide a foundation for further developments. In this paper, we study…
Let X be an irreducible, reduced complex projective hypersurface of degree d. A uniform point for X is a point P such that the projection of X from P has maximal monodromy. We extend and improve some results concerning the finiteness of the…
A classical theorem of Frankel for compact K\"ahler manifolds states that a K\"ahler S^1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when Hodge theory holds on non-compact manifolds, then…
The main purpose of this article is to present a generalization of Forelli's theorem for functions holomorphic along a suspension of integral curves of a diagonalizable vector field of aligned type. For this purpose, we develop a new…
The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions…
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…
An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to…
At the end of 1960's, Lawrence Zalcman posed a conjecture that the coefficients of univalent functions $f(z) = z + \sum\limits_2^\infty a_n z^n$ on the unit disk satisfy the sharp inequality $|a_n^2 - a_{2n-1}| \le (n-1)^2$, with equality…
Some fixed point results of classical theory, such as Banach's Fixed Point Theorem, have been previously extended by other authors to asymmetric spaces in recent years. The aim of this paper is to extend to asymmetric spaces some others…
It is a well-known result in pointfree topology that every locally compact frame is spatial. Whether this result extends to MT-algebras (McKinsey-Tarski algebras) was an open problem. We resolve it in the negative by constructing a locally…
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on…
This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
In his $1994$ survey, Kleinert defined formally and formulated the problem to obtain unit theorems for unit groups of orders in a semisimple algebra $A$. If $A$ is a group algebra $FG$, it boils down to classifying all finite groups $G$…
N. Kishore, Proc. Amer. Math. Soc. 14 (1963), 523, considered the Rayleigh functions sigma_n, sums of the negative even powers of the (non-zero) zeros of the Bessel function J_nu(z) and provided a convolution type sum formula for finding…