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Year 2016, Volume: 4 Issue: 1, 63 - 68, 15.04.2016
https://doi.org/10.36753/mathenot.421404

Abstract

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.

Some Results of Best Proximity Point in Regular Cone Metric Spaces

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

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.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

M. Chinaie This is me

N. Rajaee This is me

M. Ahmadi Baseri This is me

Publication Date April 15, 2016
Submission Date January 10, 2015
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Chinaie, M., Rajaee, N., & Baseri, M. A. (2016). Some Results of Best Proximity Point in Regular Cone Metric Spaces. Mathematical Sciences and Applications E-Notes, 4(1), 63-68. https://doi.org/10.36753/mathenot.421404
AMA Chinaie M, Rajaee N, Baseri MA. Some Results of Best Proximity Point in Regular Cone Metric Spaces. Math. Sci. Appl. E-Notes. April 2016;4(1):63-68. doi:10.36753/mathenot.421404
Chicago Chinaie, M., N. Rajaee, and M. Ahmadi Baseri. “Some Results of Best Proximity Point in Regular Cone Metric Spaces”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 63-68. https://doi.org/10.36753/mathenot.421404.
EndNote Chinaie M, Rajaee N, Baseri MA (April 1, 2016) Some Results of Best Proximity Point in Regular Cone Metric Spaces. Mathematical Sciences and Applications E-Notes 4 1 63–68.
IEEE M. Chinaie, N. Rajaee, and M. A. Baseri, “Some Results of Best Proximity Point in Regular Cone Metric Spaces”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 63–68, 2016, doi: 10.36753/mathenot.421404.
ISNAD Chinaie, M. et al. “Some Results of Best Proximity Point in Regular Cone Metric Spaces”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 63-68. https://doi.org/10.36753/mathenot.421404.
JAMA Chinaie M, Rajaee N, Baseri MA. Some Results of Best Proximity Point in Regular Cone Metric Spaces. Math. Sci. Appl. E-Notes. 2016;4:63–68.
MLA Chinaie, M. et al. “Some Results of Best Proximity Point in Regular Cone Metric Spaces”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 63-68, doi:10.36753/mathenot.421404.
Vancouver Chinaie M, Rajaee N, Baseri MA. Some Results of Best Proximity Point in Regular Cone Metric Spaces. Math. Sci. Appl. E-Notes. 2016;4(1):63-8.

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