Research Article
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Year 2015, , 25 - 35, 15.05.2015
https://doi.org/10.36753/mathenot.421205

Abstract

References

  • 1] Chang, S. S., Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 129 (2000), no. 3, 845-853.
  • [2] Chang, S. S., Cho, Y. J., Lee, B. S. and Kang, S. H., Iterative approximation of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces. J. Math. Anal. Appl. 224 (1998), 165-194.
  • [3] Chang, S. S., Cho, Y. J., and Kim, J. K., Some results for uniformly L-Lipschitzian mappings in Banach spaces. Appl. Math. Lett. 22, (2009), no. 1, 121-125.
  • [4] Goebel, K. and Kirk, W. A., A fixed point theorem for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 35 (1972), 171-174.
  • [5] Ishikawa, S., Fixed points by a new iteration method. Proc. Amer. Math. Soc. 44 (1974), 147-150.
  • [6] Kim, J. K., Sahu, D. R. and Nam, Y. M., Convergence theorem for fixed points of nearly uniformly L− Lipschitzian asymptotically generalized Φ− hemicontractive mappings. Nonlinear Anal. 71 (2009), no. 12, e2833-e2838.
  • [7] Mann, W. R., Mean value methods in iteration. Proc. Amer. Math. Soc. 4, (1953), 506-510. [8] Moore, C. and Nnoli, B. V. C., Iterative solution of nonlinear equations involving set-valued uniformly accretive operators. Comput. Math. Appl. 42 (2001), no. 1-2, 131-140.
  • [9] Mogbademu, A. A. and Xue, Z., Some convergence results for nonlinear maps in Banach spaces. Int. J. Open Problems Compt. Math. 6 (2013), 1-10.
  • [10] Mogbademu, A. A., Convergence theorem of modified Noor iteration for nonlinear maps in Banach spaces. J. Adv. Math. Stud. 7 (2014), no. 1, 56-64.
  • [11] Noor, M. A., Three-step iterative algorithms for multi-valued quasi variational inclusions. J. Math. Anal. Appl. 225 (2001), 589-604.
  • [12] Noor, M. A., Rassias, T. M. and Huang, Z., Three-step iterations for nonlinear accretive operator equations. J. Math. Anal. Appl. 274 (2002), 59-68.
  • [13] Ofoedu, E. U., Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space. J. Math. Anal. Appl. 321 (2006), 722-728.
  • [14] Olaleru, J. O. and Mogbademu, A. A., Modified Noor iterative procedure for uniformly continuous mappings in Banach spaces. Boletin de la Asociacion Matematica Venezolana Vol. XVIII (2011), no. 2, 127-135.
  • [15] Rafiq, A., Acu, A. M. and Sofonea, F., An iterative algorithm for two asymptotically pseudocontractive mappings. Int. J. Open Probl. Comput. Sci. Math. 2 (2009), no. 3, 372-382.
  • [16] Rhoades, B. E. and Soltuz, S. M., The equivalence between Mann-Ishikawa iterations and multistep iteration. Nonlinear Anal. 58 (2004), no. 1-2, 219-228.
  • [17] Schu, J., Iterative construction of fixed points of asymptotically nonexpansive mappings. J. Math. Anal. Appl. 158 (1999), 407-413.
  • [18] Sahu, D. R., Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces. Comment. Math. Univ. Carolin. 46 (2005), 653-666.
  • [19] Xue, Z., Rafiq, A. and Zhou, H., On the convergence of multi-step iteration for uniformly continuous Φ− Hemicontractive mappings. Abstr. Appl. Anal. (2012), Art. ID 386983, 9 pp.

CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS

Year 2015, , 25 - 35, 15.05.2015
https://doi.org/10.36753/mathenot.421205

Abstract

In this paper, by using the proof method of Xue, Rafiq and Zhou[19]
some strong convergence results of multi-step iterative sequence are proved for
nearly uniformly L− Lipschitzian mappings in real Banach spaces. Our results
generalise and improve some recent results in this area of research.

References

  • 1] Chang, S. S., Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 129 (2000), no. 3, 845-853.
  • [2] Chang, S. S., Cho, Y. J., Lee, B. S. and Kang, S. H., Iterative approximation of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces. J. Math. Anal. Appl. 224 (1998), 165-194.
  • [3] Chang, S. S., Cho, Y. J., and Kim, J. K., Some results for uniformly L-Lipschitzian mappings in Banach spaces. Appl. Math. Lett. 22, (2009), no. 1, 121-125.
  • [4] Goebel, K. and Kirk, W. A., A fixed point theorem for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 35 (1972), 171-174.
  • [5] Ishikawa, S., Fixed points by a new iteration method. Proc. Amer. Math. Soc. 44 (1974), 147-150.
  • [6] Kim, J. K., Sahu, D. R. and Nam, Y. M., Convergence theorem for fixed points of nearly uniformly L− Lipschitzian asymptotically generalized Φ− hemicontractive mappings. Nonlinear Anal. 71 (2009), no. 12, e2833-e2838.
  • [7] Mann, W. R., Mean value methods in iteration. Proc. Amer. Math. Soc. 4, (1953), 506-510. [8] Moore, C. and Nnoli, B. V. C., Iterative solution of nonlinear equations involving set-valued uniformly accretive operators. Comput. Math. Appl. 42 (2001), no. 1-2, 131-140.
  • [9] Mogbademu, A. A. and Xue, Z., Some convergence results for nonlinear maps in Banach spaces. Int. J. Open Problems Compt. Math. 6 (2013), 1-10.
  • [10] Mogbademu, A. A., Convergence theorem of modified Noor iteration for nonlinear maps in Banach spaces. J. Adv. Math. Stud. 7 (2014), no. 1, 56-64.
  • [11] Noor, M. A., Three-step iterative algorithms for multi-valued quasi variational inclusions. J. Math. Anal. Appl. 225 (2001), 589-604.
  • [12] Noor, M. A., Rassias, T. M. and Huang, Z., Three-step iterations for nonlinear accretive operator equations. J. Math. Anal. Appl. 274 (2002), 59-68.
  • [13] Ofoedu, E. U., Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space. J. Math. Anal. Appl. 321 (2006), 722-728.
  • [14] Olaleru, J. O. and Mogbademu, A. A., Modified Noor iterative procedure for uniformly continuous mappings in Banach spaces. Boletin de la Asociacion Matematica Venezolana Vol. XVIII (2011), no. 2, 127-135.
  • [15] Rafiq, A., Acu, A. M. and Sofonea, F., An iterative algorithm for two asymptotically pseudocontractive mappings. Int. J. Open Probl. Comput. Sci. Math. 2 (2009), no. 3, 372-382.
  • [16] Rhoades, B. E. and Soltuz, S. M., The equivalence between Mann-Ishikawa iterations and multistep iteration. Nonlinear Anal. 58 (2004), no. 1-2, 219-228.
  • [17] Schu, J., Iterative construction of fixed points of asymptotically nonexpansive mappings. J. Math. Anal. Appl. 158 (1999), 407-413.
  • [18] Sahu, D. R., Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces. Comment. Math. Univ. Carolin. 46 (2005), 653-666.
  • [19] Xue, Z., Rafiq, A. and Zhou, H., On the convergence of multi-step iteration for uniformly continuous Φ− Hemicontractive mappings. Abstr. Appl. Anal. (2012), Art. ID 386983, 9 pp.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Adesanmi Alao Mogbademu

Publication Date May 15, 2015
Submission Date April 3, 2014
Acceptance Date October 22, 2014
Published in Issue Year 2015

Cite

APA Alao Mogbademu, A. (2015). CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS. Mathematical Sciences and Applications E-Notes, 3(1), 25-35. https://doi.org/10.36753/mathenot.421205
AMA Alao Mogbademu A. CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS. Math. Sci. Appl. E-Notes. May 2015;3(1):25-35. doi:10.36753/mathenot.421205
Chicago Alao Mogbademu, Adesanmi. “CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS”. Mathematical Sciences and Applications E-Notes 3, no. 1 (May 2015): 25-35. https://doi.org/10.36753/mathenot.421205.
EndNote Alao Mogbademu A (May 1, 2015) CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS. Mathematical Sciences and Applications E-Notes 3 1 25–35.
IEEE A. Alao Mogbademu, “CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS”, Math. Sci. Appl. E-Notes, vol. 3, no. 1, pp. 25–35, 2015, doi: 10.36753/mathenot.421205.
ISNAD Alao Mogbademu, Adesanmi. “CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS”. Mathematical Sciences and Applications E-Notes 3/1 (May 2015), 25-35. https://doi.org/10.36753/mathenot.421205.
JAMA Alao Mogbademu A. CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS. Math. Sci. Appl. E-Notes. 2015;3:25–35.
MLA Alao Mogbademu, Adesanmi. “CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 1, 2015, pp. 25-35, doi:10.36753/mathenot.421205.
Vancouver Alao Mogbademu A. CONVERGENCE OF MULTI-STEP ITERATIVE SEQUENCE FOR NONLINEAR UNIFORMLY L-LIPSCHITZIAN MAPPINGS. Math. Sci. Appl. E-Notes. 2015;3(1):25-3.

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