Abstract
We prove some fixed point results for self-mapping T : X -> X in a complete G-metric space X under some contractive conditions related to a nondecreasing map phi : [0, + infinity 8) -> [0, +infinity) with lim(n -> +infinity) phi(n) (t) = 0 for all t is an element of (0, +infinity). Also, we prove the uniqueness of such fixed point, as well as studying the G-continuity of such fixed point.