On Fixed Point Theorem in Non-Archimedean Fuzzy Normed Spaces

M E Egwe

doi:10.28924/2291-8639-18-2020-99

Abstract

Let (X, N) be a non-archimedean fuzzy normed space and (X, k.k), a non-archimedean normed space where X is a linear space over a linearly ordered non-archimedean field K with a non-archimedean valuation. We give a proof of the fixed point theorem in non-archimedean Fuzzy normed space.

Highlights

Definition 1.1 [9]: A valuation is a map | · | from a field K into a non-negative reals such that (i) |a| = 0 if and only if a = 0 (ii) |ab| = |a||b| (iii) |a + b| ≤ |a| + |b| for all a, b ∈ K
We give a proof of the fixed point theorem in non-archimedean Fuzzy normed space
If the triangle inequality is replaced by a strong triangle inequality, i.e, |a+b| ≤ max(|a|, |b|) for all a, b ∈ K, the map | | is called a non-archimedean or ultrametric valuation

Summary

Introduction

Let (X, N ) be a non-archimedean fuzzy normed space and We give a proof of the fixed point theorem in non-archimedean Fuzzy normed space. If the triangle inequality is replaced by a strong triangle inequality, i.e, |a+b| ≤ max(|a|, |b|) for all a, b ∈ K, the map | | is called a non-archimedean or ultrametric valuation.

Results

Conclusion