Document Type : Research Paper
Authors
- Kamal Fallahi ^{} ^{}
- Ghasem Soleimani Rad ^{}
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
Abstract
In this paper, we prove the existence of fixed point for Chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. The main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.
Keywords
Main Subjects
[1] F. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal. (TMA)., 75 (1) (2012) 1359-1373.
[2] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, New York, 2008.
[3] Y.J. Cho, R. Saadati, and S.H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl., 61 (2011) 1254-1260.
[4] K. Fallahi and A. Aghanianas, On quasi-contractions in metric spaces with a graph, Hacettepe J. Math and Statistics., 45 (4) (2016) 1033-1047.
[5] K. Fallahi and A. Aghanianas, Chatterjea contractions in metric spaces, Int. J. Nonlinear Anal. Appl., In press.
[6] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (4) (2008) 1359-1373.
[7] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007) 1467-1475.
[8] S. Jankovic, Z. Kadelburg, and S. Radenovic, On cone metric spaces, a survey, Nonlinear Analysis., 74 (2011) 2591-2601.
[9] O. Kada, T. Suzuki, and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44 (1996) 381-391.
[10] A. Nicolae, D. O'Regan, and A. Petrusel, Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph, Georgian Math. J., 18 (2011) 307-327.
[11] H Rahimi, G Soleimani Rad, and P Kumam, A generalized distance in a cone metric space and new common fixed point results, U.P.B. Sci. Bull., (Series A). 77 (2) (2015) 195-206.
[12] H. Rahimi, G. Soleimani Rad, and P. Kumam, Generalized distance and new fixed point results, Asian-European Journal of Mathematics., 9 (2) (2016) Article ID: 1650044.
[13] S. Wang and B. Guo, Distance in cone metric spaces and common fixed point theorems, Appl. Math. Lett., 24 (2011) 1735-1739.