In this paper‎, ‎we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions‎. ‎We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spa...

In the last 10 years Open Source products have been widely used in industry. New methodologies and best practices to develop Open Source software appeared. In this work, we present an application that runs on Android-based mobile phones and collects proximity data with other devices via Bluetooth. The application gives new insights into measuring proximity inside a team of software developers. ...