Some common fixed point theorems for single valued mappings in G-ultrametric spaces


1 Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

2 aculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran


The purpose of this paper is to prove some common fixed point theorems for a single valued strongly
contractive mapping having a pair of maps on a spherically complete G-ultrametric space. c ⃝2016 All rights


[1] R. P. Agarwal, E. Karapinar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point
Theory Appl., 2013 (2013), 33 pages. 
[2] L. Gajic, M. Stojakovic, On mappings with ϕ-contractive iterate at a point on generalized metric spaces, Fixed
Point Theory Appl., 2014 (2014), 13 pages . 
[3] P. Hitzler, A. Seda, Multivalued mappings, fixed point theorems and disjunctive data bases, in: Third Irish
Workshop on Formal Methods in Computing, British Computer Society, (1999), 18 pages. 
[4] P. Hitzler, A. Seda, The fixed-point theorems of Priess-Crampe and Ribenboim in logic programming, Fields Inst.
Commun., 32 (2002), 219–235. 
[5] M. Jleli, B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl., 2012
(2012), 7 pages. 
[6] E. Karapinar, R. P. Agarwal, Further fixed point results on G-metric spaces, Fixed Point Theory Appl., 2013
(2013), 14 pages. 
[7] Z. Mustafa, A new structure for generalized metric spaces-with applications to fixed point theory, PhD thesis, the
University of Newcastle, Newcastle, UK, (2005). 
[8] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289–297.
[9] S. Priess-Crampe, Fixed points and stable balls in ultrametric spaces, Result. Math., 43 (2003), 163–167. 
[10] S. Priess-Crampe, P. Ribenboim, Differential equations over valued fields (and more), J. Reine Angew. Math.,
576 (2004), 123–147. 
[11] S. Priess-Crampe, P. Ribenboim, Systems of differential equations over valued fields, Contemp. Math., 319 (2003),
[12] S. Priess-Crampe, P. Ribenboim, The common point theorem for ultrametric spaces, Geom. Ded., 72 (1998),
[13] P. Ribenboim, Fermat's equation for matrices or quaternions over q-adic fields, Acta Arith., 113 (2004), 241–250.
[14] J. Van der Hoeven, Transseries and Real Differential Algebra, Lecture Notes in Mathematics, Springer-Verlag,
Berlin, (2006). 
[15] A. C. M. Van Rooij, Non-Archimedean Functional Analysis, Marcel Dekker, New York, (1987)