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Optimality conditions and duality for minimax fractional programming involving nonsmooth generalized univexity
Strong convergence theorems with three-step iteration in star-shaped metric spaces
1. | Department of Mathematics, Kyungsung University, Busan 608-736, South Korea |
References:
[1] |
S. S. Chang, L. Yang and X. R. Wang, Stronger convergence theroem for an infinite family of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comput., 217 (2010), 277-282.
doi: 10.1016/j.amc.2010.05.058. |
[2] |
Y. J. Cho, H. Y. Zhou and G. Guo, Weak and strong convengence theorems for three-step iteration with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 47 (2004), 707-717.
doi: 10.1016/S0898-1221(04)90058-2. |
[3] |
Hafiz Fukhar-ud-din and Safeer Hussin Khan, Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl., 328 (2007), 821-829.
doi: 10.1016/j.jmaa.2006.05.068. |
[4] |
N. J. Huang and Y. J. Cho, Fixed point theorems of compatiable mappings in convex metric spaces, Soochow J. Math., 22 (1996), 439-447. |
[5] |
A. R. Khan and M. A. Ahmed, Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications, Com. Math. Appl., 59 (2010), 2990-2995.
doi: 10.1016/j.camwa.2010.02.017. |
[6] |
A. R. Khan, A. A. Domlo and H. Fukhar-ud-din, Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 341 (2008), 1-11.
doi: 10.1016/j.jmaa.2007.06.051. |
[7] |
B. S. Lee, Strong convergence theorems with a Noor-type iterative scheme in convex metric spaces, Com. Math. Appl., 61 (2011), 3218-3225.
doi: 10.1016/j.camwa.2011.04.017. |
[8] |
Q. Y. Liu, Z. B. Liu and N. J. Huang, Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comput., 216 (2010), 883-889.
doi: 10.1016/j.amc.2010.01.096. |
[9] |
K. Nammanee and S. Suantai, The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces, Appl. Math. Comput., 187 (2007), 669-679.
doi: 10.1016/j.amc.2006.08.081. |
[10] |
M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217-229.
doi: 10.1006/jmaa.2000.7042. |
[11] |
M. A. Noor and Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., 187 (2007), 680-685.
doi: 10.1016/j.amc.2006.08.088. |
[12] |
S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 311 (2005), 506-517.
doi: 10.1016/j.jmaa.2005.03.002. |
[13] |
Y. X. Tian, Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings, Comput. Math. Appl., 49 (2005), 1905-1912.
doi: 10.1016/j.camwa.2004.05.017. |
[14] |
Y. X. Tian and C. D. Yang, Convergence theorems of three-step iterative scheme for a finite family of uniformly quasi-Lipschitzian mappings in convex metric spaces, Fixed Point Theory and Applications vol. 2009, Article ID 891967, 12pages. |
[15] |
C. Wang and L. W. Liu, Convergence theorems for fixed points of uniformly quasi-Lipschizian mappings in convex metric spaces, Nonlinear Anal. TMA, 70 (2009), 2067-2071.
doi: 10.1016/j.na.2008.02.106. |
[16] |
C. Wang, J. H. Zhu, B. Damjanovic and L. G. Hu, Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces, Appl. Math. Comput., 215 (2009), 1522-1525.
doi: 10.1016/j.amc.2009.07.006. |
[17] |
B. Xu and M. A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 267 (2002), 444-453.
doi: 10.1006/jmaa.2001.7649. |
[18] |
Y. Yao and M. A. Noor, Convergence of three-step iteration for asymptotically nonexpansive mappings, Appl. Math. Comput., 187 (2007), 883-892.
doi: 10.1016/j.amc.2006.09.008. |
show all references
References:
[1] |
S. S. Chang, L. Yang and X. R. Wang, Stronger convergence theroem for an infinite family of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comput., 217 (2010), 277-282.
doi: 10.1016/j.amc.2010.05.058. |
[2] |
Y. J. Cho, H. Y. Zhou and G. Guo, Weak and strong convengence theorems for three-step iteration with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 47 (2004), 707-717.
doi: 10.1016/S0898-1221(04)90058-2. |
[3] |
Hafiz Fukhar-ud-din and Safeer Hussin Khan, Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl., 328 (2007), 821-829.
doi: 10.1016/j.jmaa.2006.05.068. |
[4] |
N. J. Huang and Y. J. Cho, Fixed point theorems of compatiable mappings in convex metric spaces, Soochow J. Math., 22 (1996), 439-447. |
[5] |
A. R. Khan and M. A. Ahmed, Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications, Com. Math. Appl., 59 (2010), 2990-2995.
doi: 10.1016/j.camwa.2010.02.017. |
[6] |
A. R. Khan, A. A. Domlo and H. Fukhar-ud-din, Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 341 (2008), 1-11.
doi: 10.1016/j.jmaa.2007.06.051. |
[7] |
B. S. Lee, Strong convergence theorems with a Noor-type iterative scheme in convex metric spaces, Com. Math. Appl., 61 (2011), 3218-3225.
doi: 10.1016/j.camwa.2011.04.017. |
[8] |
Q. Y. Liu, Z. B. Liu and N. J. Huang, Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comput., 216 (2010), 883-889.
doi: 10.1016/j.amc.2010.01.096. |
[9] |
K. Nammanee and S. Suantai, The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces, Appl. Math. Comput., 187 (2007), 669-679.
doi: 10.1016/j.amc.2006.08.081. |
[10] |
M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217-229.
doi: 10.1006/jmaa.2000.7042. |
[11] |
M. A. Noor and Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., 187 (2007), 680-685.
doi: 10.1016/j.amc.2006.08.088. |
[12] |
S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 311 (2005), 506-517.
doi: 10.1016/j.jmaa.2005.03.002. |
[13] |
Y. X. Tian, Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings, Comput. Math. Appl., 49 (2005), 1905-1912.
doi: 10.1016/j.camwa.2004.05.017. |
[14] |
Y. X. Tian and C. D. Yang, Convergence theorems of three-step iterative scheme for a finite family of uniformly quasi-Lipschitzian mappings in convex metric spaces, Fixed Point Theory and Applications vol. 2009, Article ID 891967, 12pages. |
[15] |
C. Wang and L. W. Liu, Convergence theorems for fixed points of uniformly quasi-Lipschizian mappings in convex metric spaces, Nonlinear Anal. TMA, 70 (2009), 2067-2071.
doi: 10.1016/j.na.2008.02.106. |
[16] |
C. Wang, J. H. Zhu, B. Damjanovic and L. G. Hu, Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces, Appl. Math. Comput., 215 (2009), 1522-1525.
doi: 10.1016/j.amc.2009.07.006. |
[17] |
B. Xu and M. A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 267 (2002), 444-453.
doi: 10.1006/jmaa.2001.7649. |
[18] |
Y. Yao and M. A. Noor, Convergence of three-step iteration for asymptotically nonexpansive mappings, Appl. Math. Comput., 187 (2007), 883-892.
doi: 10.1016/j.amc.2006.09.008. |
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