We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Vald...

This paper is to serve as an introduction to the study of symmetric spaces, with the goal of describing Hermitian symmetric spaces of noncompact type. There are three basic types of symmetric space: compact, noncompact, and Euclidean, defined in terms of properties of g, the Lie algebra of its group of isometries. It turns out that a simply connected symmetric space can be described completely ...

3 Convex functions on symmetric spaces 11 3.1 Geometric preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Metric spaces with curvature bounds . . . . . . . . . . . . . . 11 3.1.2 Hadamard spaces . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 Symmetric spaces of noncompact type . . . . . . . . . . . . . 15 3.1.4 Auxiliary results . . . . . . . . . . . . . . . ....

In this paper, we prove a fixed point theorem for a pair of generalized weakly contractive mappings in complete partial metric spaces. The theorems presented are generalizations of very recent fixed point theorems due to Abdeljawad, Karapinar and Tas. To emphasize the very general nature of these results, we illustrate an example.

In this note we point out and rectify some errors in a recently published paper “N. Singh, R. Jain: Coupled Fixed Point Results For Weakly Related Mappings In Partially Ordered Metric Spaces, Bull. Iranian Math. Soc. 40 (2014), no. 1, 29-40”.

We will present an approach to deal with a problem of existence of (not) weakly invertible functions in various spaces of analytic functions in the unit ball and polydisk based on estimates for integral operators acting between functional classes of different dimensions.

This paper is an introduction to the series of papers [26, 28, 29, 30], in which we develop a combinatorial theory of certain important operads and their actions. The operads we consider are A∞ operads, E∞ operads, the little n-cubes operad and the framed little disks operad. Sections 2, 6 and 9, which can be read independently, are an introduction to the theory of operads. The reader is also r...

The aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. Our results present random versions and extensions of some well-known results in the current literature.