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Ultradiversities and their spherical completeness

Mehrabani Gholamreza H., Nourouzi Kourosh

Journal of Applied Analysis

2020

Vol. 26, nr 2

231--240

Diversities are a generalization of metric spaces which associate a positive real number to every finite subset of the space. In this paper, we introduce ultradiversities which are themselves simultaneously diversities and a sort of generalization of ultrametric spaces. We also give the notion of spherical completeness for ultradiversities based on the balls defined in such spaces. In particular, with the help of nonexpansive mappings defined between ultradiversities, we show that an ultradiversity is spherically complete if and only if it is injective.

Some fixed point theorems for G-nonexpansive mappings on ultrametric spaces and non-Archimedean normed spaces with a graph

Mamghaderi H., Masiha H. P.

Journal of Mathematics and Applications

2016

Vol. 39

81--90

A very interesting approach in the theory of fixed point is some general structures was recently given by Jachymski by using the context of metric spaces endowed with a graph. The purpose of this article is to present some new fixed point results for G-nonexpansive mappings defined on an ultrametric space and non-Archimedean normed space which are endowed with a graph. In particular, we investigate the relationship between weak connectivity graph and the existence of fixed point for these mappings.