5 papers
Proximinal sets and connectedness in graphs
Karim Chaira, Oleksiy Dovgoshey
Let be a graph with a vertex set . The graph is path-proximinal if there are a semimetric and disjoint proximinal subsets of the se…
Bipartite graphs and best proximity pairs
Karim Chaira, Oleksiy Dovgoshey, Samih Lazaiz
We say that a bipartite graph with fixed parts , is proximinal if there is a semimetric space such that and are disjoint proximinal subsets of …
Best proximity pairs in ultrametric spaces
K. Chaira, O. Dovgoshey, S. Lazaiz
In the present paper, we study the existence of best proximity pairs in ultrametric spaces. We show, under suitable assumptions, that the proximinal pair has a best proximi…
Best proximity points in ultrametric spaces
Karim Chaira, Samih Lazaiz
In the present paper, we study the existence of best proximity pair in ultrametric spaces. We show, under suitable assumptions, that the proximinal pair has a best proximit…
On Caristi fixed point theorem for set-valued mappings
Karim Chaira, Soumia Chaira, Samih Lazaiz
The aim of this paper is to discuss Penot's problem on a generalization of Caristi's fixed point theorem. We settle this problem in the negative and we present some new theorems on…