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Year 2017, , 36 - 44, 30.10.2017
https://doi.org/10.36753/mathenot.421734

Abstract

References

  • [1] Al-Thagafi, M. A., Shahzad, N., Convergence and existence result for best proximity points. Nonliner Analysis, Theory, Methods and Applications. 70 (2009), no. 10, 3665-3671.
  • [2] Eldred, A. A., Veeramani, P., Existence and convergence of best proximity points. J. Math. Anal. Appl. 323 (2006), no. 2, 1001-1006.
  • [3] Gabeleh, M., Abkar, A., Best proximity points for semi-cyclic contractive pairs in Banach spaces. Int. Math. Forum. 6 (2011), no. 44, 2179-2186.
  • [4] Haghi, R. H., Rakocevi´c, V., Rezapour, Sh., Shahzad, N., Best proximity result in regular cone metric space. ˜ Rendiconti del circolo Mathematico di palermo Co. 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] Karapinar, E., Best proximity points of cyclic mappings. Appl. Math. 25 (2012), no. 11, 1761-1766.
  • [8] Kumar, L., Som T., Existence of best proximity points in regular cone Metric Spaces. Azerbaijan Journal of Mathematics. 5 (2015), no. 1, 44-53.
  • [9] Lee, B. S., Cone metric version of existence and convergence for best proximity points. Universal J. Appl. Math. 2 (2014), no. 2, 104-108.
  • [10] Rezapour, Sh., Best approximations in cone metric spaces. Mathematica moravica. 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] Thakur, B. S., Sharma, A., Existence and convergence of best proximity points for semi-cyclic contraction pairs. International Journal of Analysis and Applications. 5 (2014), no. 1, 33-44.

Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces

Year 2017, , 36 - 44, 30.10.2017
https://doi.org/10.36753/mathenot.421734

Abstract

The aim of this paper is to establish some conditions which guarantee the existence of best proximity for
semi-cyclic contraction pairs in regular cone metric spaces. We obtain best proximity points and prove
convergence results for such maps in regular cone metric spaces.

References

  • [1] Al-Thagafi, M. A., Shahzad, N., Convergence and existence result for best proximity points. Nonliner Analysis, Theory, Methods and Applications. 70 (2009), no. 10, 3665-3671.
  • [2] Eldred, A. A., Veeramani, P., Existence and convergence of best proximity points. J. Math. Anal. Appl. 323 (2006), no. 2, 1001-1006.
  • [3] Gabeleh, M., Abkar, A., Best proximity points for semi-cyclic contractive pairs in Banach spaces. Int. Math. Forum. 6 (2011), no. 44, 2179-2186.
  • [4] Haghi, R. H., Rakocevi´c, V., Rezapour, Sh., Shahzad, N., Best proximity result in regular cone metric space. ˜ Rendiconti del circolo Mathematico di palermo Co. 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] Karapinar, E., Best proximity points of cyclic mappings. Appl. Math. 25 (2012), no. 11, 1761-1766.
  • [8] Kumar, L., Som T., Existence of best proximity points in regular cone Metric Spaces. Azerbaijan Journal of Mathematics. 5 (2015), no. 1, 44-53.
  • [9] Lee, B. S., Cone metric version of existence and convergence for best proximity points. Universal J. Appl. Math. 2 (2014), no. 2, 104-108.
  • [10] Rezapour, Sh., Best approximations in cone metric spaces. Mathematica moravica. 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] Thakur, B. S., Sharma, A., Existence and convergence of best proximity points for semi-cyclic contraction pairs. International Journal of Analysis and Applications. 5 (2014), no. 1, 33-44.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

M. Ahmadi Baseri This is me 0000-0003-4997-6576

H. Mazaheri This is me 0000-0003-3450-3776

Publication Date October 30, 2017
Submission Date January 3, 2017
Published in Issue Year 2017

Cite

APA Baseri, M. A., & Mazaheri, H. (2017). Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces. Mathematical Sciences and Applications E-Notes, 5(2), 36-44. https://doi.org/10.36753/mathenot.421734
AMA Baseri MA, Mazaheri H. Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces. Math. Sci. Appl. E-Notes. October 2017;5(2):36-44. doi:10.36753/mathenot.421734
Chicago Baseri, M. Ahmadi, and H. Mazaheri. “Best Proximity Points for Semi-Cyclic Contraction Pairs in Regular Cone Metric Spaces”. Mathematical Sciences and Applications E-Notes 5, no. 2 (October 2017): 36-44. https://doi.org/10.36753/mathenot.421734.
EndNote Baseri MA, Mazaheri H (October 1, 2017) Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces. Mathematical Sciences and Applications E-Notes 5 2 36–44.
IEEE M. A. Baseri and H. Mazaheri, “Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces”, Math. Sci. Appl. E-Notes, vol. 5, no. 2, pp. 36–44, 2017, doi: 10.36753/mathenot.421734.
ISNAD Baseri, M. Ahmadi - Mazaheri, H. “Best Proximity Points for Semi-Cyclic Contraction Pairs in Regular Cone Metric Spaces”. Mathematical Sciences and Applications E-Notes 5/2 (October 2017), 36-44. https://doi.org/10.36753/mathenot.421734.
JAMA Baseri MA, Mazaheri H. Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces. Math. Sci. Appl. E-Notes. 2017;5:36–44.
MLA Baseri, M. Ahmadi and H. Mazaheri. “Best Proximity Points for Semi-Cyclic Contraction Pairs in Regular Cone Metric Spaces”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 2, 2017, pp. 36-44, doi:10.36753/mathenot.421734.
Vancouver Baseri MA, Mazaheri H. Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces. Math. Sci. Appl. E-Notes. 2017;5(2):36-44.

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