Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2015, Cilt: 3 Sayı: 1, 25 - 35, 15.05.2015
https://doi.org/10.36753/mathenot.421205

Öz

Kaynakça

  • 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

Yıl 2015, Cilt: 3 Sayı: 1, 25 - 35, 15.05.2015
https://doi.org/10.36753/mathenot.421205

Öz

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.

Kaynakça

  • 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.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Adesanmi Alao Mogbademu

Yayımlanma Tarihi 15 Mayıs 2015
Gönderilme Tarihi 3 Nisan 2014
Kabul Tarihi 22 Ekim 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

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. Mayıs 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, sy. 1 (Mayıs 2015): 25-35. https://doi.org/10.36753/mathenot.421205.
EndNote Alao Mogbademu A (01 Mayıs 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, c. 3, sy. 1, ss. 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 (Mayıs 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, c. 3, sy. 1, 2015, ss. 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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