Title: On Weak and Strong Convergence Theorems of Modified SP-Iteration Scheme for Total Asymptotically Nonexpansive Mappings
Author(s): G. S. Saluja
Pages: 24-39
Cite as:
G. S. Saluja, On Weak and Strong Convergence Theorems of Modified SP-Iteration Scheme for Total Asymptotically Nonexpansive Mappings, Int. J. Anal. Appl., 10 (1) (2016), 24-39.

Abstract


In this paper, we study modified SP-iteration scheme for three total asymptotically nonexpansive mappings and also establish some weak and strong convergence theorems for mentioned mappings and scheme to converge to common fixed points in the framework of Banach spaces. Our results extend and generalize the previous works from the current existing literature.

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References


  1. R. P. Agarwal, Donal O’Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, Nonlinear Convex Anal. 8(1)(2007), 61–79. Google Scholar

  2. Ya. I. Albert, C. E. Chidume, H. Zegeye, Approximating fixed point of total asymptotically nonexpansive mappings, Fixed Point Theory Appl. (2006) Art. ID 10673. Google Scholar

  3. R. E. Bruck, T. Kuczumow, S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math. 65(1993), 169–179. Google Scholar

  4. C. E. Chidume, E. U. Ofoedu, Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings, J. Math. Anal. Appl. 333(2007), 128–141. Google Scholar

  5. J. Garcia Falset, W. Kaczor, T. Kuczumow, S. Reich, Weak convergence theorems for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal., TMA, 43(3)(2001), 377–401. Google Scholar

  6. K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35(1)(1972), 171–174. Google Scholar

  7. R. Glowinski, P. Le Tallec, Augemented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, Siam, Philadelphia, (1989). Google Scholar

  8. S. Haubruge, V. H. Nguyen, J. J. Strodiot, Convergence analysis and applications of the Glowinski Le Tallec splitting method for finding a zero of the sum of two maximal monotone operators, J. Optim. Theory Appl. 97(1998), 645–673. Google Scholar

  9. S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 44(1974), 147–150. Google Scholar

  10. W. A. Kirk, Fixed point theorems for non-lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339–346. Google Scholar

  11. N. Maiti, M. K. Ghosh, Approximating fixed points by Ishikawa iterates, Bull. Aust. Math. Soc. 40(1989), 113–117. Google Scholar

  12. W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4(1953), 506–510. Google Scholar

  13. M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251(1)(2000), 217–229. Google Scholar

  14. M. A. Noor, Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl. 255(2001), 589–604. Google Scholar

  15. Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73(1967), 591–597. Google Scholar

  16. W. Phuengrattana, S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math. 235(2011), 3006–3014. Google Scholar

  17. J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43(1)(1991), 153–159. Google Scholar

  18. H. F. Senter, W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44(1974), 375–380. Google Scholar

  19. K. Sitthikul, S. Saejung, Convergence theorems for a finite family of nonexpansive and asymptotically nonex- pansive mappings, Acta Univ. Palack. Olomuc. Math. 48(2009), 139–152. Google Scholar

  20. K. K. Tan, H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178(1993), 301–308. Google Scholar

  21. B. L. Xu, M. A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267(2002), 444–453. Google Scholar


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