# $F_{m}$-contractive and $F_{m}$-expanding mappings in $M$-metric spaces

Volume 18, Issue 3, pp 262--271 Publication Date: March 22, 2018       Article History
• 167 Views

### Authors

Nabil Mlaiki - Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

### Abstract

Inspired by the work of Górnicki in his recent article [J. Górnicki, Fixed Point Theory Appl., ${\bf 2017}$ (2017), 10 pages], where he introduced a new class of self mappings called $F$-expanding mappings, in this paper we introduce the concept of $F_{m}$-contractive and $F_{m}$-expanding mappings in $M$-metric spaces. Also, we prove the existence and uniqueness of fixed point for such mappings.

### Keywords

• $M$-metric spaces
• $F_{m}$-contractive
• $F_{m}$-expanding mappings

### References

• [1] K. Abodayeh, N. Mlaiki, T. Abdeljawad, W. Shatanawi , Relations between partial metric spaces and M-metric spaces, Caristi Kirk’s Theorem in M-metric type spaces , J. Math. Anal., 7 (2016), 1–12.

• [2] M. Asadi, E. Karapınar, P. Salimi , New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014 (2014 ), 9 pages.

• [3] J. Górnicki , Fixed points theorems for F-expanding mappings , Fixed Point Theory Appl., 2017 (2017), 10 pages.

• [4] R. H. Haghi, S. Rezapour, N. Shahzad , Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450–454.

• [5] S. G. Matthews, Partial metric topology, Ann. New York Acad. Sci., 728 (1994), 183–197.

• [6] N. Mlaiki, N. Souayah, K. Abodayeh, T. Abdeljawad , Contraction principles in Ms-metric spaces , J. Nonlinear Sci. Appl., 10 (2017), 575–582.

• [7] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012 ), 6 pages.