2010/07/19 by Hüseyi̇n Çakallı, Cakalli, Huseyin, Ayşe Sönmez +3
Decision Sciences · Mathematics · #46A04 #47H04 #54A05 #57N17 #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Fuzzy and Soft Set Theory #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.1007.3123
openalex publication_date 2010/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis 72 2259-2261] to investigate the equivalence of vectorial versions of fixed point theorems of contractive mappings in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense. In this paper we find out that the topology induced by topological vector space valued cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e any topological vector space valued cone metric space is metrizable.