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Статья
2021

Strong and Weak Convergence Theorems for General Mixed Equilibrium, General Variational Inequality, and Fixed Point Problems for Two Nonexpansive Semigroups in Hilbert Spaces


Baoshuai ZhangBaoshuai Zhang, Ying TianYing Tian
Российский физический журнал
https://doi.org/10.1007/s11182-021-02412-4
Abstract / Full Text

In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of the general mixed equilibrium problem and a general variational inequality for two cocoercive mappings and the set of common fixed points of two nonexpansive semigroups in Hilbert space. We obtain both strong and weak convergence theorems for the sequences generated by these iterative processes in Hilbert spaces. Our results improve and extend the results obtained elsewhere.

Author information
  • School of Economics and Management, Chongqing Normal University, Chongqing, ChinaBaoshuai Zhang & Ying Tian
References
  1. A. Tada and W. Takahashi, J. Optim. Theory Appl., 133, No. 3, 359–370 (2007).
  2. L. C. Ceng and J. C. Yao, J. Comput. Appl. Math., 214, No. 1, 186–201 (2008).
  3. J. W. Peng and J. C. Yao, Taiwanese J. Math., 12, No. 1, 1401–1432 (2008).
  4. S. Plubtieng and R. Punpaeng, Appl. Math. Comput., 197, No. 2, 548–558 (2008).
  5. S. Takahashi and W. Takahashi, Nonlinear Anal., 69, No. 3, 1025–1033 (2008).
  6. Y. Yao, Y. C. Liou, and S. M. Kang, Comput. Math. with Appl., 59, No. 11, 3472–3480 (2010).
  7. L. C. Ceng and J. C. Yao, Nonlinear Anal.,72, No. 3, 1922–1937 (2010).
  8. X. Qin, S. S. Chang, and Y. J. Cho, Nonlinear Anal. Real World Appl., 11, No. 4, 2963–2972 (2009).
  9. S. S. Chang, H. W. J. Lee, and C. K. Chan, Nonlinear Anal., 70, No. 9, 3307–3319 (2009).
  10. X. Qin, M. Shang, and Y. Su, Math. Comput. Model., 48, No. 7, 1033–1046 (2008).
  11. X. Qin, Y. J. Cho, and S. M. Kang, J. Comput. Appl. Math., 225, No. 6, 20–30 (2009).
  12. J. W. Peng and J. C. Yao, Comput. Math. with Appl., 58, No. 5, 1287–1301 (2009).
  13. P. Kumam, Nonlinear Anal. Hybrid Syst., 2, No. 4, 1245–1255 (2008).
  14. C. Jaiboon, W. Chantarangsi, and P. Kumamb, Nonlinear Anal. Hybrid Syst., 4, No. 1, 199–215 (2010).
  15. C. Jaiboon, P. Kumam, and U. W. Humphries, Bull. Malaysian Math. Sci. Soc., 32, No. 2, 173–185 (2009).
  16. R. U. Verma, Math. Sci. Res. Hotline, 3, No. 8, 65–68 (1999).
  17. W. Kumam, P. Kumam, Nonlinear Anal. Hybrid Syst., 3, 640–656 (2009).
  18. S. Thianwan, Nonlinear Anal. Hybrid Syst., 3, No. 4, 605–614 (2009).
  19. A. Kangtunyakarn and S. Suantai, Nonlinear Anal., 71, No. 10, 4448—4460 (2009).
  20. G. Cai and C. S. Hu, Nonlinear Anal. Hybrid Syst., 2, No. 4, 395–407 (2009).
  21. H. He and R. Chen, Fixed Point Theory Appl., 65, No. 6, 6342–6350 (2007).
  22. K. Wattanawitoon and P. Kumam, Fixed Point Theory Appl., 65, No. 6, 1247–1259 (2009).
  23. K. S. Al–Ghafri and H. Rezazadeh, AMNS, 4, No. 2, 289–304 (2019).
  24. M. Modanli and A. Akgul, AMNS, 5, No. 1, 163–170 (2020).
  25. S. Saejung, Fixed Point Theory Appl., 132, No. 1, 214–221 (2008).
  26. F. E. Browder, Arch. Ration. Mech. Anal., 24, No. 1, 82–89 (1967).
  27. M. Eslamian and A. Abkar, Top, 22, No. 2, 554–570 (2014).
  28. M. Eslamian, RACSAM, 107, 299–307 (2013).
  29. A. Latif and M. Eslamian, Abstr. Appl. Anal., 2013, No. 1, 548–558 (2013).
  30. K. Goebel and W. A. Kirk, in: Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge (1990), pp: 135–136.
  31. Z. Opial, Bull. Amer. Math. Soc., 73, No. 4, 561–597 (1967).
  32. W. Takahashi and M. Toyoda, J. Optim. Theory Appl., 118, No. 2, 417–428 (2003).
  33. L. C. Ceng, C. Wang, and J. C. Yao, Math. Methods Oper. Res., 67, No. 3, 375–390 (2008).
  34. Y. J. Cho, H. Zhou, and G. Guo, Comput. Math. with Appl., 47, No. 4, 707–717 (2004).
  35. P. Kumam, J. Appl. Math. Comput., 29, No. 7, 263–280 (2009).