Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces

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 φ: [ 0,+∞)→ [ 0,+∞) with lim n→+∞φ n (t)= 0 for all tε(0,+∞). Also, we prove the uniqueness of such fixed point, as well as studying the G -continuity of such fixed point. Copyright © 2010 W. Shatanawi.