Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 2 Sayı: 3, 125 - 135, 01.10.2019

Öz

Kaynakça

  • [1] F.E. Browder, Fixed point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad . (1965)53, 1272-1276.
  • [2] W.R. Mann, Mean value methods on iteration, Proc. Amer. Math. Soc . (1953)4, 506-510.
  • [3] S.Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. (1974)44, 147-150.
  • [4] Y.F.Su, X.L.Qin, Strong convergence of modified Ishikawa iterations for nonlinear mappings, Proceedings MathematicalSciences.(2007)1,117, 97-107.
  • [5] B.Javad, Weak and strong convergence theorems of modified Ishikawa iteration for an infinitely countable family of pointwiseasymptotically nonexpansive mappings in Hilbert spaces, Arab Journal of Mathematical Sciences. (2011) 17, 153-169.
  • [6] K.Phayap,et.al, Strong Convergence theorems of modified Ishikawa iterative method for an infinite family of strict pseudocontractionsin Banach spaces, International Journal of Mathematics and Mathematical Sciences. (2011) Article ID 549364,18.
  • [7] W.Kriengsak, K.Poom, Convergence theorems of modified Ishikawa iterative scheme for two nonexpansive semigroups, FixedPoint Theory and Applications. (2010) Article ID 914702, 12.
  • [8] S.S.Chang,et.al, The equivalence between the convergence of modified Picard, modified mann, and modified Ishikawa iterations,Mathematical and Computer Modelling. (2003)37, 985-991.
  • [9] J.Z.Chen, D.P.Wu, Convergence theorems of modified Mann iterations, Fixed Point Theory and Applications. (2013)2013,1, 282.
  • [10] M.A.Noor, New approximation schemes for general variational inequalities, J.Math.Anal.Appl. (2000)251, 217-229.
  • [11] W.Phuengrattana, S.Suantai, On the rate of convergence of Mann, Ishikawa,Noor and SP-iterations for continuous functionson arbitrary interval, Journalof Computational and Applied Mathematics. (2011)235, 3006-3014.
  • [12] T.Suzuki, On strong convergence to a common fixed point of nonexpansive semigroup in Hilbert spaces, Proc. Amer. Math.Soc.(2003)131,7, 371-379.
  • [13] H.K.Xu, A strong convergence theorem for contraction semigroups in Banach spaces, Bull Austral Math Soc,(2005)72,371-379.
  • [14] N.Shioji,W.Takahashi, Strong convergence theorems for asymptotically nonexpansive semigroups in Hilbert spaces, NonlinearAnalysis. (1998)34, 87-99.
  • [15] J.B.Baillon, Un theoreme de type ergodic pour les contrations nonlineares dans unespace de Hilbert,C.r.heba.Seanc.Acad.Sci.Paris. (1975)280, 1511-1514.
  • [16] K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptoticallynonexpansive mappings, J. Math. Anal. Appl. (2006)314, 320-334.
  • [17] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc.(1991)43, 153-159.
  • [18] H.F. Senter, W.G. Dotson,Jr, Approximating fixed points of non-expansive mappings, Proc. Amer. Math. Soc. (1974)44,375-380.
  • [19] R.Chen, Y.Song, Convergence to common fixed point of nonexpansive semigroups, J. Math. Anal. Appl. (2007)200,566-575.

Convergence theorems of modified Ishikawa iterations in Banach spaces

Yıl 2019, Cilt: 2 Sayı: 3, 125 - 135, 01.10.2019

Öz

In this paper, we introduce the modified iterations of Ishikawa type for nonexpansive mappings (nonexpansive semigroups) to have the strong convergence in a uniformly convex Banach space. We study the approximation of common fixed point of nonexpansive mappings and nonexpansive semigroups in Banach space by using a new iterative scheme.

Kaynakça

  • [1] F.E. Browder, Fixed point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad . (1965)53, 1272-1276.
  • [2] W.R. Mann, Mean value methods on iteration, Proc. Amer. Math. Soc . (1953)4, 506-510.
  • [3] S.Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. (1974)44, 147-150.
  • [4] Y.F.Su, X.L.Qin, Strong convergence of modified Ishikawa iterations for nonlinear mappings, Proceedings MathematicalSciences.(2007)1,117, 97-107.
  • [5] B.Javad, Weak and strong convergence theorems of modified Ishikawa iteration for an infinitely countable family of pointwiseasymptotically nonexpansive mappings in Hilbert spaces, Arab Journal of Mathematical Sciences. (2011) 17, 153-169.
  • [6] K.Phayap,et.al, Strong Convergence theorems of modified Ishikawa iterative method for an infinite family of strict pseudocontractionsin Banach spaces, International Journal of Mathematics and Mathematical Sciences. (2011) Article ID 549364,18.
  • [7] W.Kriengsak, K.Poom, Convergence theorems of modified Ishikawa iterative scheme for two nonexpansive semigroups, FixedPoint Theory and Applications. (2010) Article ID 914702, 12.
  • [8] S.S.Chang,et.al, The equivalence between the convergence of modified Picard, modified mann, and modified Ishikawa iterations,Mathematical and Computer Modelling. (2003)37, 985-991.
  • [9] J.Z.Chen, D.P.Wu, Convergence theorems of modified Mann iterations, Fixed Point Theory and Applications. (2013)2013,1, 282.
  • [10] M.A.Noor, New approximation schemes for general variational inequalities, J.Math.Anal.Appl. (2000)251, 217-229.
  • [11] W.Phuengrattana, S.Suantai, On the rate of convergence of Mann, Ishikawa,Noor and SP-iterations for continuous functionson arbitrary interval, Journalof Computational and Applied Mathematics. (2011)235, 3006-3014.
  • [12] T.Suzuki, On strong convergence to a common fixed point of nonexpansive semigroup in Hilbert spaces, Proc. Amer. Math.Soc.(2003)131,7, 371-379.
  • [13] H.K.Xu, A strong convergence theorem for contraction semigroups in Banach spaces, Bull Austral Math Soc,(2005)72,371-379.
  • [14] N.Shioji,W.Takahashi, Strong convergence theorems for asymptotically nonexpansive semigroups in Hilbert spaces, NonlinearAnalysis. (1998)34, 87-99.
  • [15] J.B.Baillon, Un theoreme de type ergodic pour les contrations nonlineares dans unespace de Hilbert,C.r.heba.Seanc.Acad.Sci.Paris. (1975)280, 1511-1514.
  • [16] K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptoticallynonexpansive mappings, J. Math. Anal. Appl. (2006)314, 320-334.
  • [17] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc.(1991)43, 153-159.
  • [18] H.F. Senter, W.G. Dotson,Jr, Approximating fixed points of non-expansive mappings, Proc. Amer. Math. Soc. (1974)44,375-380.
  • [19] R.Chen, Y.Song, Convergence to common fixed point of nonexpansive semigroups, J. Math. Anal. Appl. (2007)200,566-575.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Shengquan Weng Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA Weng, S. (2019). Convergence theorems of modified Ishikawa iterations in Banach spaces. Results in Nonlinear Analysis, 2(3), 125-135.
AMA Weng S. Convergence theorems of modified Ishikawa iterations in Banach spaces. RNA. Ekim 2019;2(3):125-135.
Chicago Weng, Shengquan. “Convergence Theorems of Modified Ishikawa Iterations in Banach Spaces”. Results in Nonlinear Analysis 2, sy. 3 (Ekim 2019): 125-35.
EndNote Weng S (01 Ekim 2019) Convergence theorems of modified Ishikawa iterations in Banach spaces. Results in Nonlinear Analysis 2 3 125–135.
IEEE S. Weng, “Convergence theorems of modified Ishikawa iterations in Banach spaces”, RNA, c. 2, sy. 3, ss. 125–135, 2019.
ISNAD Weng, Shengquan. “Convergence Theorems of Modified Ishikawa Iterations in Banach Spaces”. Results in Nonlinear Analysis 2/3 (Ekim 2019), 125-135.
JAMA Weng S. Convergence theorems of modified Ishikawa iterations in Banach spaces. RNA. 2019;2:125–135.
MLA Weng, Shengquan. “Convergence Theorems of Modified Ishikawa Iterations in Banach Spaces”. Results in Nonlinear Analysis, c. 2, sy. 3, 2019, ss. 125-3.
Vancouver Weng S. Convergence theorems of modified Ishikawa iterations in Banach spaces. RNA. 2019;2(3):125-3.