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Existence and convergence results for best proximity points in cone metric spaces
| 1. | Department of Mathematics, Kyungsung University, Busan 608-736 |
References:
| [1] |
M. A. Al-Thagafi and N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis, 70 (2009), 3665-3671.
doi: 10.1016/j.na.2008.07.022. |
| [2] |
M. A. Al-Thagafi and N. Shahzad, Best proximity sets and equilibrium pairs for a finite family of mulimaps, Fixed Point Theory Appl., Article ID 457069, 10 pages, 10 (2008). |
| [3] |
M. A. Al-Thagafi and N. Shahzad, Best proximity pairs and equilibrium pairs for Kakutani multimaps, Nonlinear Analysis, 70 (2009), 1209-1216.
doi: 10.1016/j.na.2008.02.004. |
| [4] |
S. S. Basha, Best proximity point theorems: resolution of an important non-linear programming problem, Optim. Lett., 7 (2013), 1167-1177.
doi: 10.1007/s11590-012-0493-5. |
| [5] |
A. A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 232 (2006), 1001-1006.
doi: 10.1016/j.jmaa.2005.10.081. |
| [6] |
K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 122 (1969), 234-240. |
| [7] |
M. Gabeleh and A. Abkar, Best proximity points for semi-cyclic contractive pairs in Banach spaces, Int. Math. Forum, 6 (2011), 2179-2186. |
| [8] |
L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476.
doi: 10.1016/j.jmaa.2005.03.087. |
| [9] |
S. Karpagam and S. Agrawal, Best proximity point theorems for p-cyclic Meir-Keeler contraction, Fixed Point Theory Appl., Art. ID 197308, 9 (2009). |
| [10] |
W. K. Kim, S. Kum and K. H. Lee, On general best proximity pairs and equilibrium pairs in free abstract economies, Nonlinear Analysis, 68 (2008), 2216-2227.
doi: 10.1016/j.na.2007.01.057. |
| [11] |
W. A. Kirk, S. Reich and P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Func. Anal. Optim., 24 (2003), 851-862.
doi: 10.1081/NFA-120026380. |
| [12] |
B. S. Lee, Cone metirc version of existence and convergence for best proximity points, Universal J. Appl. Math., 2 (2014), 104-108. |
| [13] |
C. Mongkalkeha and P. Kumam, Some common best proximity points for proximity commuting mappings, Optim. Lett., 7 (2013), 1825-1826.
doi: 10.1007/s11590-012-0525-1. |
| [14] |
D. Turkoglu, M. Abuloha and T. Abdeljawad, KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear Analysis, 72 (2010), 348-353.
doi: 10.1016/j.na.2009.06.058. |
| [15] |
D. Xu and L. Deng, Cone semi-metric spaces and fixed point theorems for generalized weak contractive mappings, Nonlinear Analysis Forum, 18 (2013), 57-64. |
show all references
References:
| [1] |
M. A. Al-Thagafi and N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis, 70 (2009), 3665-3671.
doi: 10.1016/j.na.2008.07.022. |
| [2] |
M. A. Al-Thagafi and N. Shahzad, Best proximity sets and equilibrium pairs for a finite family of mulimaps, Fixed Point Theory Appl., Article ID 457069, 10 pages, 10 (2008). |
| [3] |
M. A. Al-Thagafi and N. Shahzad, Best proximity pairs and equilibrium pairs for Kakutani multimaps, Nonlinear Analysis, 70 (2009), 1209-1216.
doi: 10.1016/j.na.2008.02.004. |
| [4] |
S. S. Basha, Best proximity point theorems: resolution of an important non-linear programming problem, Optim. Lett., 7 (2013), 1167-1177.
doi: 10.1007/s11590-012-0493-5. |
| [5] |
A. A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 232 (2006), 1001-1006.
doi: 10.1016/j.jmaa.2005.10.081. |
| [6] |
K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 122 (1969), 234-240. |
| [7] |
M. Gabeleh and A. Abkar, Best proximity points for semi-cyclic contractive pairs in Banach spaces, Int. Math. Forum, 6 (2011), 2179-2186. |
| [8] |
L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476.
doi: 10.1016/j.jmaa.2005.03.087. |
| [9] |
S. Karpagam and S. Agrawal, Best proximity point theorems for p-cyclic Meir-Keeler contraction, Fixed Point Theory Appl., Art. ID 197308, 9 (2009). |
| [10] |
W. K. Kim, S. Kum and K. H. Lee, On general best proximity pairs and equilibrium pairs in free abstract economies, Nonlinear Analysis, 68 (2008), 2216-2227.
doi: 10.1016/j.na.2007.01.057. |
| [11] |
W. A. Kirk, S. Reich and P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Func. Anal. Optim., 24 (2003), 851-862.
doi: 10.1081/NFA-120026380. |
| [12] |
B. S. Lee, Cone metirc version of existence and convergence for best proximity points, Universal J. Appl. Math., 2 (2014), 104-108. |
| [13] |
C. Mongkalkeha and P. Kumam, Some common best proximity points for proximity commuting mappings, Optim. Lett., 7 (2013), 1825-1826.
doi: 10.1007/s11590-012-0525-1. |
| [14] |
D. Turkoglu, M. Abuloha and T. Abdeljawad, KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear Analysis, 72 (2010), 348-353.
doi: 10.1016/j.na.2009.06.058. |
| [15] |
D. Xu and L. Deng, Cone semi-metric spaces and fixed point theorems for generalized weak contractive mappings, Nonlinear Analysis Forum, 18 (2013), 57-64. |
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