Title: Convergence of a Modified Multi-Step Iterative Scheme for p- Nearly Uniformly L-Lipschitzian Asymptotically Pseudocontrative Mappings
Author(s): V.O. Olisama, A.A. Mogbademu, J.O. Olaleru
Pages: 192-200
Cite as:
V.O. Olisama, A.A. Mogbademu, J.O. Olaleru, Convergence of a Modified Multi-Step Iterative Scheme for p- Nearly Uniformly L-Lipschitzian Asymptotically Pseudocontrative Mappings, Int. J. Anal. Appl., 4 (2) (2014), 192-200.

Abstract


In this paper, it is shown that the modified multi-step iteration converges strongly to the common fixed point of a finite family of nearly uniformly L- Lipschitzian asymptotically pseudocontractive mappings. The main result is an improvement and extension of well known results in the literature.


Full Text: PDF

 

References


  1. S. S. Chang, Some results for asymptotically pseudocontractive mappings and asymptotically nonexpansive mappings , Proc. Amer. Math. Soc., 129(2001), 845-853.

  2. S. S. Chang, Y. J. Cho and J. K. Kim, Some results for uniformly L- Lipschitzian mappings in Banach spaces, Applied Mathematics Letters, 22(2009), 121-125.

  3. K. Deimling, Functional analysis, Springer, Berlin(1980).

  4. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. soc., 35(1972),171-174.

  5. S. Ishikawa, Fixed point for a new iterative method, Proc. Amer. Math. Soc. 44(1974), 147-150.

  6. W. R. Mann, Mean value method in iteration, Proc. Amer. Math. Soc. 4(1953), 506-510.

  7. A. A. Mogbademu, Modified multi-step iterative methods for a family of p - strongly pseudocontractive maps, Bulletin of Mathematical Analysis and Application, 4(2012), 83-90.

  8. A .A. Mogbademu, Modified Noor iterative procedure for three asymptoticallly pseudocontractive maps, International Journal of Open Problems Compt., Mathematics, 6(2013), 95- 102.

  9. C. Moore and B. V. C. Nnoli, Iterative solution of nonlinear equations involving set-valued uniformly accretive operators, Comput. Math. Anal.and Appl., 42(2001), 131-140.

  10. M. A. Noor, Three steps iterative algorithms for multi-valued quasi variational inclusions, Jour. Math. Anal. Appl., 225(2001), 589-604.

  11. E. U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian and asymptotically nonexpansive mapping in Banach space, Jour.of Math. Anal. and Appl., 321(2006), 722-728.

  12. J. O. Olaleru and A.A. Mogbademu, Modified Noor iterative procedure for uniformly continuous mappings in Banach space, Boletin de la Asociacion Matematica Venezolana, 18(2011), 127.

  13. B. E. Rhoades, S. M. Soltuz, The equivalence between Mann-Ishikawa iterations and multistep iteration, Nonlinear Analysis Theory, Methods and Applications, 58(2004), 219-228.

  14. D. R. Sahu, Fixed point of Demicontinuos nearly Lipschitzian mappings in Banach spaces, Comment Math.Univ.Carolin.46, 4(2005), 653-666.

  15. J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, Jour.of Math. and Appl., 158(1999), 407-413.

  16. B. S. Tharkur, Strong convergence for asymptotically generalised Φ -Hemicontractive mappings, ROMAI J. 8(2012), 165-171.

  17. Zhique Xue and Guiwen Lv, Strong convergence theorems for uniformly L- Lipschitzian asymptotically pseudocontractive mappings in Banach spaces Xue and Lv Jour. of Ineq. and Appl.. (2013) 1/79.