Ruang Metrik Vektor dan Teorema titik tetap dari Fungsi-Φ dada Ruang Metrik Vektor

Abstract

In this final project, we introduce ϕ-function on positive cone of a Riesz space. We also learn about vector metric space which includes the definition and examples, characteristics, and convergence of sequences in vector metric spaces. Moreover, we prove fixed point theorems of ϕ-function on a Riesz space in vector metric space by using direct proof. Our results generalize the main results of the Banach contraction principle in which the constant k ∈ (0,1) is replaced by ϕ-function on Riesz space, also the metric spaces is replaced by vector metric spaces.