Best Proximity Point In A locally Convex Vector Space And Application

Brahim Saadaoui; Samih Lazaiz; Mohamed Aamri; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 216

Best Proximity Point In A locally Convex Vector Space And Application

Brahim Saadaoui, Samih Lazaiz, Mohamed Aamri

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 31, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: A.Anthony Eldred, W. A. Kirk and P. Veermani have established the existence of best proximity pairs for a relatively nonexpansive mapping in Banach space [1]. Ha Duc Vuong has established a fixed point theorem for nonexpansive mapping in locally convex space and apply it to get a fixed point theorem in probabilistic normed space[2]. In this work, first we proved the existence of best proximity points for a relatively nonexpansive mapping in a locally convex space and we apply it to get a best proximity pairs theorem in a probabilistic normed space.