Year 2017,
, 36 - 44, 30.10.2017
M. Ahmadi Baseri
H. Mazaheri
References
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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.
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- [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
M. Ahmadi Baseri
H. Mazaheri
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.