A general fixed point theorem for mappings satisfying an phi - implicit relation in complete G - metric spaces

Authors : Valeriu Popa, Alina-mihaela Patriciu

Pages : 403-408

View : 14 | Download : 6

Publication Date : 2012-04-17

Article Type : Other

Abstract :In this paper a general fixed point theorem for mappings satisfying an phi - implicit relation is proved, which generalize the results from [3] and [13]. In [4], [5] Dhage introduced a new class of generalized  metric space, called D - metric space. Mustafa and Sims  [12], [13] proved that most of the claims concerning the  fundamental topological structures of D - metric spaces  are incorrect and introduced an appropriate notion of  generalized metric space, named G - metric space. In  fact, Mustafa and other authors [3], [7] – [15], [18]  studied many fixed point results for self mappings in a  G - metric space under certain conditions. In [6] and  [18] some fixed point theorems for mappings satisfying  φ - maps are proved. In [16], [17], Popa initiated the  study of fixed points for mappings satisfying implicit  relations. In [2] Altun and Turkoglu introduced a new  type of implicit relations satisfying a φ - map. The  purpose of this paper is to prove a general fixed point  theorem in G - metric spaces for mappings satisfying an  φ - implicit relation which generalize the results from  [3] and [14].   
Keywords : fixed point, G - metric space, implicit relation, phi - implicit relation