Related papers: Short note on Smithson's paper concerning Arzel\`a…
An $L^2$ version of the classical Denjoy-Carleman theorem regarding quasi-analytic functions was proved by P. Chernoff on $\mathbb R^n$ using iterates of the Laplacian. We give a simple proof of this theorem which generalizes the result on…
We show that on almost complex surfaces plurisubharmonic functions can be locally approximated by smooth plurisubharmonic functions. The main tool is the Poletsky type theorem due to U. Kuzman.
The paper introduces the concept of quasimeasure of noncompactness. Motivated by the Arzel\`a-Ascoli theorem for $C^b(X,E)$, where $X$ is an Euclidean space and $E$ an arbitrary Banach space, we construct a quasimeasure for this space and…
In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…
Let $X$ be a locally compact topological space, $(Y,d)$ be a boundedly compact metric space and $LB(X,Y)$ be the space of all locally bounded functions from $X$ to $Y$. We characterize compact sets in $LB(X,Y)$ equipped with the topology of…
This study is motivated by a series of recent papers that show that, if a given deterministic sequence in the unit interval has a Poisson pair correlation function, then the sequence is uniformly distributed. Analogous results have been…
This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. P\'ales, building on their introduction of the triangle function concept in [J. Nonlinear Convex Anal, Vol 18 (3), 515-524 (2017)]. By applying…
The aim of the present article is to render the spectral theory of mean values of automorphic $L$-functions -- in a unified fashion. This is an outcome of the investigation commenced with the parts XII and XIV, where a framework was laid on…
We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…
Given an m-dimensional compact submanifold $\mathbf{M}$ of Euclidean space $\mathbf{R}^s$, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general $\mathbf{R}^s$-valued functionals…
This paper discusses, certain algebraic, analytic, and topological results on partial iterated function systems($IFS_p$'s). Also, the article proves the Collage theorem for partial iterated function systems. Further, it provides a method to…
The class of O-metric spaces generalize several existing metric-types in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and…
The theory of admissible distributions over a weight-space of one-variable was studied by Amice--V\'{e}lu and played important roles in the cyclotomic Iwasawa theory of non-ordinary p-adic Galois representations. In this article, we discuss…
$L$-functions can be viewed axiomatically, such as in the formulation due to Selberg, or they can be seen as arising from cuspidal automorphic representations of $\textrm{GL}(n)$, as first described by Langlands. Conjecturally these two…
In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. The obtained results extend,…
This article has a twofold purpose. On the one hand I would like to draw attention to some nice exercises on the Kepler laws, due to Otto Laporte from 1970. Our discussion here has a more geometric flavour than the original analytic…
In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially…
This is an exposition of homotopical results on the geometric realization of semi-simplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The…
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the…