Isaac Scientific Publishing

Advances in Analysis

New Contractive Conditions for Maps in G-metric Type Spaces

Download PDF (497 KB) PP. 61 - 67 Pub. Date: October 25, 2016

DOI: 10.22606/aan.2016.12001


  • Yaé Ulrich Gaba*
    Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa


In this article, we introduce a new type of contractive self maps defined in G-metric type spaces and prove a common fixed point theorem. We establish that under the convergence of a certain series, a family of self maps have a common fixed point.


G-metric type space, fixed point


[1] Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete g-metric spaces,” Fixed point theory and Applications, vol. 2008, no. 1, pp. 1–12, 2008.

[2] Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and convex Analysis, vol. 7, no. 2, pp. 289–297, 2006.

[3] B. C. Dhage, “Generalised metric space and mappings with fixed point,” 1992.

[4] Y. U. Gaba, “-sequences and fixed point theorem in G-metric type spaces,” 2016, manuscript submitted for publication.

[5] ——, “Metric type spaces and -sequences,” Quaestiones Mathematicae, (in press).

[6] O. S. Iyiola and Y. U. Gaba, “On metric type spaces and fixed point theorems,” Applied Mathematical Sciences, vol. 8, no. 79, pp. 3905–3920, 2014.

[7] M. Jleli and B. Samet, “Remarks on g-metric spaces and fixed point theorems,” Fixed Point Theory and Applications, vol. 2012, no. 1, pp. 1–7, 2012.

[8] S. K. Mohanta, “Some fixed point theorems in g-metric spaces,” An. Stiint. Univ. Ovidius, Constanta. Ser. Mat, vol. 20, no. 1, pp. 285–306, 2012.