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Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

Citations

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Cited by:

  1. Shin-ya Matsushita & Li Xu, 2014. "On Finite Convergence of Iterative Methods for Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 701-715, June.
  2. Prasit Cholamjiak & Suthep Suantai, 2013. "Iterative methods for solving equilibrium problems, variational inequalities and fixed points of nonexpansive semigroups," Journal of Global Optimization, Springer, vol. 57(4), pages 1277-1297, December.
  3. Z. Y. Huang & M. A. Noor, 2012. "Studies on Common Solutions of a Variational Inequality and a Fixed-Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 525-535, August.
  4. Lu-Chuan Ceng & Nicolas Hadjisavvas & Ngai-Ching Wong, 2010. "Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems," Journal of Global Optimization, Springer, vol. 46(4), pages 635-646, April.
  5. S. Plubtieng & T. Thammathiwat, 2010. "A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities," Journal of Global Optimization, Springer, vol. 46(3), pages 447-464, March.
  6. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
  7. Y. Kimura & W. Takahashi & J. C. Yao, 2011. "Strong Convergence of an Iterative Scheme by a New Type of Projection Method for a Family of Quasinonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 239-253, May.
  8. A. Tada & W. Takahashi, 2007. "Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 359-370, June.
  9. Vahid Darvish, 2016. "Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 584-603, September.
  10. Yanlai Song & Luchuan Ceng, 2013. "A general iteration scheme for variational inequality problem and common fixed point problems of nonexpansive mappings in q-uniformly smooth Banach spaces," Journal of Global Optimization, Springer, vol. 57(4), pages 1327-1348, December.
  11. Satit Saejung & Kanokwan Wongchan, 2011. "A note on Ceng-Wang-Yao’s result [Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Meth. Oper. Res. (2008) 67: 375–390]," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 153-157, April.
  12. S. Takahashi & W. Takahashi & M. Toyoda, 2010. "Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 27-41, October.
  13. Lu-Chuan Ceng & Chang-yu Wang & Jen-Chih Yao, 2008. "Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 375-390, June.
  14. Nakajo, Kazuhide, 2015. "Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 251-258.
  15. Yuanheng Wang & Mingyue Yuan & Bingnan Jiang, 2021. "Multi-Step Inertial Hybrid and Shrinking Tseng’s Algorithm with Meir–Keeler Contractions for Variational Inclusion Problems," Mathematics, MDPI, vol. 9(13), pages 1-13, July.
  16. Z. Y. Huang & M. A. Noor & E. Al-Said, 2010. "On an Open Question of Takahashi for Nonexpansive Mappings and Inverse Strongly Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 194-204, October.
  17. Ming Tian & Meng-Ying Tong, 2019. "Extension and Application of the Yamada Iteration Algorithm in Hilbert Spaces," Mathematics, MDPI, vol. 7(3), pages 1-13, February.
  18. Lili Chen & Ni Yang & Jing Zhou, 2020. "Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
  19. Xiaolong Qin & Sun Cho & Shin Kang, 2011. "An extragradient-type method for generalized equilibrium problems involving strictly pseudocontractive mappings," Journal of Global Optimization, Springer, vol. 49(4), pages 679-693, April.
  20. Yonghong Yao & Yeong-Cheng Liou & Shin Kang, 2010. "Minimization of equilibrium problems, variational inequality problems and fixed point problems," Journal of Global Optimization, Springer, vol. 48(4), pages 643-656, December.
  21. W. Takahashi, 2013. "Strong Convergence Theorems for Maximal and Inverse-Strongly Monotone Mappings in Hilbert Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 781-802, June.
  22. Habtu Zegeye & Naseer Shahzad, 2012. "Strong convergence of an iterative method for pseudo-contractive and monotone mappings," Journal of Global Optimization, Springer, vol. 54(1), pages 173-184, September.
  23. Yonghong Yao & Ke Wang & Xiaowei Qin & Li-Jun Zhu, 2019. "Extension of Extragradient Techniques for Variational Inequalities," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
  24. Suthep Suantai & Narin Petrot & Montira Suwannaprapa, 2019. "Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces," Mathematics, MDPI, vol. 7(11), pages 1-21, October.
  25. Xiaolong Qin & Lai-Jiu Lin & Shin Min Kang, 2011. "On a Generalized Ky Fan Inequality and Asymptotically Strict Pseudocontractions in the Intermediate Sense," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 553-579, September.
  26. L. Zeng & J. Yao, 2009. "A hybrid extragradient method for general variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 141-158, March.
  27. Yekini Shehu, 2012. "Iterative method for fixed point problem, variational inequality and generalized mixed equilibrium problems with applications," Journal of Global Optimization, Springer, vol. 52(1), pages 57-77, January.
  28. J. W. Peng, 2010. "Iterative Algorithms for Mixed Equilibrium Problems, Strict Pseudocontractions and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 107-119, January.
  29. Ying Liu & Hang Kong, 2019. "Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 1049-1065, December.
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