FIXED POINT FOR QUASI-CONTRACTIONS IN METRIC SPACESENDOWED WITH A GRAPH

In the present work, we introduce G-quasi-contractions using directed graphs in metric spaces with a graphand we show that this contraction generalizes a large number of contractions. We then investigate the existenceof fixed points for G-quasi-contractions under two different conditions and discuss the main theorem.Finally, we list some consequences of our theorem where either the contractive condition is replaced witha stronger one or the underlying space is changed to a complete metric space or a complete cone metric space.