Generalized normed spaces and Fixed point Theorems
Classical Analysis and ODEs
2018-09-26 v1 Functional Analysis
Abstract
G\"ahler ([4],[5]) introduced and investigated the notion of 2-metric spaces and 2-normed spaces in sixties. These concepts are inspired by the notion of area in two dimensional Euclidean space. In this paper, we choose a fundamentally different approach and introduce a possible generalization of usual norm retaining the distance analogue properties. This generalized norm will be called as -norm. We show that every -normed space is a -metric space and therefore, a topological space and develop the theory for -normed spaces. We also introduce -Banach spaces and obtain some fixed point theorems.
Cite
@article{arxiv.1809.09486,
title = {Generalized normed spaces and Fixed point Theorems},
author = {Kamran Alam Khan},
journal= {arXiv preprint arXiv:1809.09486},
year = {2018}
}