Banach Contractive Mapping Theorem on Partially Ordered Sets Equipped with Vector Metric

Year 2025, Volume: 17 Issue: 2 , 586 - 594 , 30.12.2025

Şehla Eminoğlu

https://doi.org/10.47000/tjmcs.1567340

https://izlik.org/JA25UJ58TW

Abstract

In this paper, left (right) vector metric convergence and left (right) vector metric continuity are defined
using the positive and negative parts of a vector-valued metric. These definitions and the obtained new results are applied to the Banach Contractive Mapping Theorem and examined within the framework of order structures, such as partially ordered sets, Archimedean spaces, and Dedekind complete spaces.

Keywords

Left (right) vector metric convergence , left (right) vector metric continuity , positive (negative) part of vector metric , partially ordered set , dedekind complete spaces , fixed point

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