Research Communication | Open Access
Volume 2021 | Communication ID 224
Volume 2021 | Communication ID 224
| Best proximity points in locally convex spaces endowed with a graph |
Brahim Saadaoui, Samih Lazaiz, Mohamed Aamri
Received |
Accepted |
Published |
January 31, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: Fixed point theorems deal with conditions under wich maps have invariant points, [1, 3, 4, 8]. In other words, we are searching for an element in the domain of the mapping, whose image is as close to it as possible. It is worth to note that the best proximity point theorems can be viewed as a generalization of fixed point theorems, [1]. In this paper, we consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph G. For that, we introduce the notions of non-self G-contraction, [7] and G-nonexpansive mappings and we show that for each semi-norm ...