Best proximity point theory on vector metric spaces

Authors : Hakan ŞAHİN

Pages : 130-142

Doi:10.31801/cfsuasmas.780723

View : 7 | Download : 31

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :In this paper, we first give a new definition of Ω-Dedekind complete Riesz space insert ignore into journalissuearticles values(E,≤); in the frame of vector metric space insert ignore into journalissuearticles values(Ω,ρ,E); and we investigate the relation between Dedekind complete Riesz space and our new concept. Moreover, we introduce a new contraction so called α-vector proximal contraction mapping. Then, we prove certain best proximity point theorems for such mappings in vector metric spaces insert ignore into journalissuearticles values(Ω,ρ,E); where insert ignore into journalissuearticles values(E,≤); is Ω-Dedekind complete Riesz space. Thus, for the first time, we acquire best proximity point results on vector metric spaces. As a result, we generalize some fixed point results proved in both vector metric spaces and partially ordered vector metric spaces such as main results of V4 . Further, we provide nontrivial and comparative examples to show the effectiveness of our main results.
Keywords : Best proximity point, α admissible, proximal contraction, vector metric spaces