Some Results of Best Proximity Point in Regular Cone Metric Spaces

Year 2016, Volume: 4 Issue: 1, 63 - 68, 15.04.2016

M. Chinaie N. Rajaee M. Ahmadi Baseri

https://doi.org/10.36753/mathenot.421404

Abstract

The purpose of this paper is to provide sufficient conditions for the existence of a best proximity point for
various types of cyclic contraction maps. Our results extend and improve certain recent results in the
literature.

Keywords

Best proximity point , cyclic contraction map , cone L- function , regular cone metric

References

• [1] Al-Thagafi, M. A., Shahzad, N., Convergence and existence result for best proximity points. Nonliner Anal. 70 (2009), no.10, 3665-3671.
• [2] Amini-Harandi, A., Hussain, N., Akbar, F., Best proximity point results for generalized contractions in metric spaces. Fixed Point Theory Appl. (2013), 2013:164, 13 pp.
• [3] Eldred, A. A., Veeramani, P., Existence and convergence of best proximity points. J. Math. Anal. Appl. 323 (2006), no.2, 1001-1006.
• [4] Haghi, R. H., Rakocevic, V., Rezapour, Sh., Shahzad, N., Best proximity result in regular cone metric space. ˜ Rend. Circ. Mat. Palermo (2) 60 (2011), no.3, 323-327.
• [5] Haghi, R. H., Rezapour, Sh., Fixed points of multifunctions on regular cone metric space. Expo. Math. 28 (2010), no.1, 71-77.
• [6] Huang, L. G., Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2007), no.2, 1468-1476.
• [7] Karapınar, E., Best proximity points of cyclic mappings. Appl. Math. Lett. 25 (2012), no.11, 1761-1766.
• [8] Kirk, W. A., Sirinavasan, P. S., Veeramani, P., Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4 (2003), no.1, 79 - 89.
• [9] Mohsenalhosseini, S. A. M, Mazaheri, H., Dehghan, M. A., Approximate best proximity pairs in metric space. Abstr. Appl. Anal. (2011), Art. ID 596971, 9 pp.
• [10] Rezapour, Sh., Best approximations in cone metric spaces. Math. Morav. 11 (2007), 85-88.
• [11] Rezapour, Sh., Hamlbarani Haghi, R., Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings". J. Math. Anal. Appl. 345 (2008), no.2, 719-724.
• [12] Turkoglu, D., Abuloha, M., Cone metric spases and fixed point theorems in diametrically contractive mappings. Acta Mathematica Sinica, English Series. 26 (2010), no.3, 489-496.