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A strong convergence result for systems of nonlinear operator equations involving total asymptotically nonexpansive mappings in uniformly convex Banach spaces

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove the strong convergence of an implicit iterative procedure to a solution of a system of nonlinear operator equations involving total asymptotically nonexpansive operators in uniformly convex Banach spaces.
Rocznik
Strony
27--48
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
  • Mathematics Department, Faculty of Science, Assiut University, Egypt
Bibliografia
  • 1. Alber Ya.I., Chidume C.E., Zegeye H.: Approximating fixed points of total asymptotically nonexpansive mappings. Fixed Point Theory Appl. 2006 (2006), article ID 10673.
  • 2. Bruck R.E., Kuczumow T., Reich S.: Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property. Colloq. Math. LXV, fasc. 2 (1993), 169–179.
  • 3. Chang S.S. , Cho Y. J., Zhou H.: Demiclosedness principle and weak convergence theorems for asymptotically nonexpansive mappings. J. Korean Math. Soc. 38 (2001), 1245–1260.
  • 4. Chidume C.E.: Nonexpansive mappings, generalizations and iterative algorithms. In: Agarwal R.P., O’Reagan D. (eds.), Nonlinear Analysis and Application. To V. Lakshmikantam on his 80th Birthday, Kluwer Academic Publ., Dordrecht 2003, 383–430.
  • 5. Chidume C.E., Bashir A.: Approximation of common fixed points for finite families of nonself asymptotically nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 326 (2007), 960–973.
  • 6. Chidume C.E., Ofoedu E.U.: Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings. J. Math. Anal. Appl. 333 (2007), 128–141.
  • 7. Chidume C.E., Ofoedu E.U., Zegeye H.: Strong and weak convergence theorems for asymptotically nonexpansive mappings. J. Math. Anal. Appl. 280 (2003), 364–374.
  • 8. Chidume C.E., Shahzaad N.: Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings. Nonlinear Anal. 62 (2005), 1149–1156.
  • 9. Goebel K., Kirk W.A.: A fixed point theorem for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 35 (1972), 171–174.
  • 10. Kaczor W.: Weak convergence of almost orbits of asymptotically nonexpansive semigroups. J. Math. Anal. Appl. 272 (2002), 565–574.
  • 11. Kirk W.A.: Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type. Israel J. Math. 17 (1974), 339–346.
  • 12. Mann W.R.: Mean value methods in iteration. Proc. Amer. Math. Soc. 4 (1953), 506–510.
  • 13. Matsuhita S.Y., Kuroiwa D.: Strong convergence of averaging iteration of nonexpansive nonself mappings. J. Math. Anal. Appl. 294 (2004), 206–214.
  • 14. Osilike M.O., Udomene A.: Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings. Math. Comput. Modelling 32 (2000), 1181–1191.
  • 15. Plubteing S., Wangkeeree R.: Strong convergence theorems for three-step iterations with errors non-Lipschitzian nonself mappings in Banach spaces. Comput. Math. Appl. 51 (2006), 1093–1102.
  • 16. Rashwan R.A., Abdel Hakim A.A.: Generalized three-step iteration schemes and common fixed points of three asymptotically quasi-nonexpansive mappings. Demonstratio Math. 41 (2008), 895–908.
  • 17. Rashwan R.A., Abdel Hakim A.A.: On the convergence of modified explicit iterations with errors for finite families of non-self mappings in banach spaces. JP J. Fixed Point Theory Appl. 3 (2008), 13–37.
  • 18. Rashwan R.A., Rafiq A., Abdel Hakim A.A.: On the convergence of three-step iteration process with errors in the class of quasi-contractive operators. Proc. Pakistan Acad. Sci. 46, no. 1 (2009), 41–46.
  • 19. Reich S.: Weak convergence theorems for nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 67 (1979), 274–276.
  • 20. Rhoades B.E.: Fixed point iterations for certain nonlinear mappings. J. Math. Anal. Appl. 183 (1994), 118–120.
  • 21. Schu J.: Weak and strong convergence of fixed points of asymptotically nonexpansive mappings. Bull. Austral. Math. Soc. 43 (1991), 153–159.
  • 22. Shahzad N.: Approximating fixed points of nonself nonexpansive mappings in Banach spaces. Nonlinear Anal. 61 (2005), 1031–1039.
  • 23. Takahashi W., Tamura T.: A convergence theorem for a pair of nonexpansive mappings. J. Conv. Anal.5 (1998), 45–56.
  • 24. Tan K.K., Xu H.K.: The nonlinear ergodic theorem for asymptotically nonexpansive mappings in Banach space. Proc. Amer. Math. Soc. 114 (1992), 399–404.
  • 25. Tan K.K., Xu H.K.: Approximating fixed points of nonexpansive mappings by Ishikawa iteration process. J. Math. Anal. Appl. 178 (1993), 301–308.
  • 26. Tan K.K., Xu H.K.: Fixed point iteration processes for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 122 (1994), 733–739.
  • 27. Tian Y.X., Chang S.S., Huang J.L.: On the approximation problem of common fixed points for a finite family of non-self asymptotically quasi-nonexpansive type mappings in Banach spaces. Comput. Math. Appl. 53 (2007), 1847–1853.
  • 28. Wang L.: Strong and weak convergence theorems for nonself asymptotically nonexpansive mappings. J. Math. Anal. Appl. 323 (2006), 550–557.
  • 29. Xu H.K., Yin X.M.: Strong convergence theorems for nonexpansive nonself mappings. Nonlinear Anal. 24 (1995), 223–228.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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