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Year 2021, Volume: 4 Issue: 1, 47 - 56, 31.03.2021
https://doi.org/10.53006/rna.793940

Abstract

References

  • [1] Charles,Chidume.;Geometric Properties of Banach Spaces and Nonlinear Itera- tions.(2009)
  • [2] Zhiqun Xue,Guiwen Lvand BE Rhoades;the convergence theorems of Ishikawa itera- tive process with errors for hemi-contractive mappings in uniformly smooth Banach spaces,Xue et al. Fixed Point Theory and Applications 2012, 2012:206.
  • [3] Phayap Katchang, Poom Kumam;Strong convergence of the modified Ishikawa itera- tive method for infinitely many nonexpansive mappings in Banach spaces,Computers and Mathematics with Applications 59 (2010) 1473–1483.
  • [4] Abebe R. Tufa and H. Zegeye;Mann and Ishikawa-Type Iterative Schemes for Ap- proximating Fixed Points of Multi-valued Non-Self Mappings,Springer International Publishing 2016.
  • [5] Godwin Amechi Okeke;Convergence analysis of the Picard–Ishikawa hybrid iterative process with applications,African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019.
  • [6] Xu, YG: Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations. J. Math. Anal. Appl. 224, 91-101 (1998).
  • [7] Liu, L.; Ishikawa and Mann iterative process with errors for nonlinear strongly accre- tive mappings in Banach spaces, J. Math. Anal. Appl. 194(1995), no. 1, 114–125.
  • [8] Xu, Y.; Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91–101.
  • [9] Cudia, D. F.; The theory of Banach spaces: Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284–314.
  • [10] Browder, FE: Nonlinear operators and nonlinear equations of evolution in Banach spaces. In: Proc. Of Symposia in Pure Math., Vol. XVIII, Part 2 (1976).

The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings

Year 2021, Volume: 4 Issue: 1, 47 - 56, 31.03.2021
https://doi.org/10.53006/rna.793940

Abstract

Charles[1] proved the convergence of Picard-type iterative
for generalized Φ− accretive non-self maps in a real uniformly smooth
Banach space.
Based on the theorems of the zeros of strongly Φ− quasi-
accretive and fixed points of strongly Φ− hemi-contractions, we extend
the results to Ishikawa iterative and Ishikawa iteration process with er-
rors for generalized Φ− hemi-contractive maps .

References

  • [1] Charles,Chidume.;Geometric Properties of Banach Spaces and Nonlinear Itera- tions.(2009)
  • [2] Zhiqun Xue,Guiwen Lvand BE Rhoades;the convergence theorems of Ishikawa itera- tive process with errors for hemi-contractive mappings in uniformly smooth Banach spaces,Xue et al. Fixed Point Theory and Applications 2012, 2012:206.
  • [3] Phayap Katchang, Poom Kumam;Strong convergence of the modified Ishikawa itera- tive method for infinitely many nonexpansive mappings in Banach spaces,Computers and Mathematics with Applications 59 (2010) 1473–1483.
  • [4] Abebe R. Tufa and H. Zegeye;Mann and Ishikawa-Type Iterative Schemes for Ap- proximating Fixed Points of Multi-valued Non-Self Mappings,Springer International Publishing 2016.
  • [5] Godwin Amechi Okeke;Convergence analysis of the Picard–Ishikawa hybrid iterative process with applications,African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019.
  • [6] Xu, YG: Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations. J. Math. Anal. Appl. 224, 91-101 (1998).
  • [7] Liu, L.; Ishikawa and Mann iterative process with errors for nonlinear strongly accre- tive mappings in Banach spaces, J. Math. Anal. Appl. 194(1995), no. 1, 114–125.
  • [8] Xu, Y.; Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91–101.
  • [9] Cudia, D. F.; The theory of Banach spaces: Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284–314.
  • [10] Browder, FE: Nonlinear operators and nonlinear equations of evolution in Banach spaces. In: Proc. Of Symposia in Pure Math., Vol. XVIII, Part 2 (1976).
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Linxin Li This is me

Dingping Wu This is me

Publication Date March 31, 2021
Published in Issue Year 2021 Volume: 4 Issue: 1

Cite

APA Li, L., & Wu, D. (2021). The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings. Results in Nonlinear Analysis, 4(1), 47-56. https://doi.org/10.53006/rna.793940
AMA Li L, Wu D. The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings. RNA. March 2021;4(1):47-56. doi:10.53006/rna.793940
Chicago Li, Linxin, and Dingping Wu. “The Convergence of Ishikawa Iteration for Generalized Φ-Contractive Mappings”. Results in Nonlinear Analysis 4, no. 1 (March 2021): 47-56. https://doi.org/10.53006/rna.793940.
EndNote Li L, Wu D (March 1, 2021) The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings. Results in Nonlinear Analysis 4 1 47–56.
IEEE L. Li and D. Wu, “The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings”, RNA, vol. 4, no. 1, pp. 47–56, 2021, doi: 10.53006/rna.793940.
ISNAD Li, Linxin - Wu, Dingping. “The Convergence of Ishikawa Iteration for Generalized Φ-Contractive Mappings”. Results in Nonlinear Analysis 4/1 (March 2021), 47-56. https://doi.org/10.53006/rna.793940.
JAMA Li L, Wu D. The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings. RNA. 2021;4:47–56.
MLA Li, Linxin and Dingping Wu. “The Convergence of Ishikawa Iteration for Generalized Φ-Contractive Mappings”. Results in Nonlinear Analysis, vol. 4, no. 1, 2021, pp. 47-56, doi:10.53006/rna.793940.
Vancouver Li L, Wu D. The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings. RNA. 2021;4(1):47-56.