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Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C)

Year 2017, Volume: 66 Issue: 1, 51 - 65, 01.02.2017
https://doi.org/10.1501/Commua1_0000000774

Abstract

The aim of this paper is to introduce an iterative process witherrors for a finite family of multivalued mappings satisfying the condition (C)which is weaker than non-expansiveness. We also prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces

References

  • A. Abkar, M. Eslamian, Fixed point theorems for Suzuki generalized nonexpansive multi- valued mappings in Banach spaces, Fixed Point Theory and Applications. 2010, Article ID 457935, 10 pp (2010).
  • S.S. Chang, Y.K. Tang, L. W. Y.G. Xu, Y.H Zhao, G. Wang, Convergence theorems for some multi-valued generalized nonexpansive mappings, Fixed Point Theory and Applications. 2014, 2014:33.
  • Y.J. Cho, H. Zhou, G. Gou, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 47 (2004) 707- 717.
  • E.L. Dozo, Multivalued nonexpansive mappings and Opial’s condition, Proc. Amer. Math. Soc., 38 (1973) 286-292.
  • M. Eslamian, A. Abkar, One- step iterative process for a …nite family of multivalued mappings, Math. Comput. Modell., 54 (2011) 105-111.
  • M. Eslamian, S. Homaeipour, Strong convergence of three-step iterative process with erors for three multivalued mappings, arXiv.1105.2149v1 [math.FA] (2011).
  • S. H. Khan, M Abbas, S. Ali, Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process, Acta Mathematica Sinica, English Series, July 2014, Vol. 30, Issue 7, pp1231-1241.
  • S. H. Khan, I. Yildirim, Fixed points of multivalued nonexpansive mappings in Banach spaces, Fixed Point Theory and Applications 2012, 2012:73
  • J. T. Markin, Continuous dependence of …xed point sets, Proc. Amer. Math. Soc., 38 (1973) 545-547.
  • S. B. Nadler, Jr., Multivalued contraction mappings, Paci…c J. Math., 30 (1969) 475-488.
  • Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967) 591–597.
  • B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 54 (2007) 872-877.
  • K. P. R. Sastry, G. V. R. Babu, Convergence of Ishikawa iterates for a multivalued mapping with a …xed point, Czechoslovak Math. J., 55 (2005) 817-826.
  • Y. Song, Y. J. Cho, Some notes on Ishikawa iteration for mul-tivalued mappings. Bull Korean Math Soc 48(3):575–584(2011). doi:10.4134/BKMS.2011.48.3.575
  • N. Shahzad, H. Zegeye, On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. 71 (2009) 838-844.
  • T. Suzuki, Fixed point thoerems and convergence theorems for some generelized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095.
  • K. K. Tan, H. K. Xu, Approximating …xed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993) 301-308.
  • I. Yildirim, M. Ozdemir, Approximating Common Fixed Points of Asymptotically Quasi- Nonexpansive Mappings by a New Iterative Process, Arab J Sci Eng (2011) 36:393–403.
  • I. Yildirim, M. Ozdemir, A new iterative process for common …xed points of …nite families of non-self-asymptotically non-expansive mappings, Nonlinear Analysis, 71 (2009) 991-999.
Year 2017, Volume: 66 Issue: 1, 51 - 65, 01.02.2017
https://doi.org/10.1501/Commua1_0000000774

Abstract

References

  • A. Abkar, M. Eslamian, Fixed point theorems for Suzuki generalized nonexpansive multi- valued mappings in Banach spaces, Fixed Point Theory and Applications. 2010, Article ID 457935, 10 pp (2010).
  • S.S. Chang, Y.K. Tang, L. W. Y.G. Xu, Y.H Zhao, G. Wang, Convergence theorems for some multi-valued generalized nonexpansive mappings, Fixed Point Theory and Applications. 2014, 2014:33.
  • Y.J. Cho, H. Zhou, G. Gou, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 47 (2004) 707- 717.
  • E.L. Dozo, Multivalued nonexpansive mappings and Opial’s condition, Proc. Amer. Math. Soc., 38 (1973) 286-292.
  • M. Eslamian, A. Abkar, One- step iterative process for a …nite family of multivalued mappings, Math. Comput. Modell., 54 (2011) 105-111.
  • M. Eslamian, S. Homaeipour, Strong convergence of three-step iterative process with erors for three multivalued mappings, arXiv.1105.2149v1 [math.FA] (2011).
  • S. H. Khan, M Abbas, S. Ali, Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process, Acta Mathematica Sinica, English Series, July 2014, Vol. 30, Issue 7, pp1231-1241.
  • S. H. Khan, I. Yildirim, Fixed points of multivalued nonexpansive mappings in Banach spaces, Fixed Point Theory and Applications 2012, 2012:73
  • J. T. Markin, Continuous dependence of …xed point sets, Proc. Amer. Math. Soc., 38 (1973) 545-547.
  • S. B. Nadler, Jr., Multivalued contraction mappings, Paci…c J. Math., 30 (1969) 475-488.
  • Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967) 591–597.
  • B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 54 (2007) 872-877.
  • K. P. R. Sastry, G. V. R. Babu, Convergence of Ishikawa iterates for a multivalued mapping with a …xed point, Czechoslovak Math. J., 55 (2005) 817-826.
  • Y. Song, Y. J. Cho, Some notes on Ishikawa iteration for mul-tivalued mappings. Bull Korean Math Soc 48(3):575–584(2011). doi:10.4134/BKMS.2011.48.3.575
  • N. Shahzad, H. Zegeye, On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. 71 (2009) 838-844.
  • T. Suzuki, Fixed point thoerems and convergence theorems for some generelized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095.
  • K. K. Tan, H. K. Xu, Approximating …xed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993) 301-308.
  • I. Yildirim, M. Ozdemir, Approximating Common Fixed Points of Asymptotically Quasi- Nonexpansive Mappings by a New Iterative Process, Arab J Sci Eng (2011) 36:393–403.
  • I. Yildirim, M. Ozdemir, A new iterative process for common …xed points of …nite families of non-self-asymptotically non-expansive mappings, Nonlinear Analysis, 71 (2009) 991-999.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

İsa Yıldırım This is me

Publication Date February 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 1

Cite

APA Yıldırım, İ. (2017). Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C). Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 51-65. https://doi.org/10.1501/Commua1_0000000774
AMA Yıldırım İ. Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C). Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2017;66(1):51-65. doi:10.1501/Commua1_0000000774
Chicago Yıldırım, İsa. “Strong and Weak Convergence of an Iterative Process for a Finite Family of Multivalued Mappings Satisfying the Condition (C)”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 1 (February 2017): 51-65. https://doi.org/10.1501/Commua1_0000000774.
EndNote Yıldırım İ (February 1, 2017) Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C). Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 51–65.
IEEE İ. Yıldırım, “Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C)”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 1, pp. 51–65, 2017, doi: 10.1501/Commua1_0000000774.
ISNAD Yıldırım, İsa. “Strong and Weak Convergence of an Iterative Process for a Finite Family of Multivalued Mappings Satisfying the Condition (C)”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (February 2017), 51-65. https://doi.org/10.1501/Commua1_0000000774.
JAMA Yıldırım İ. Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C). Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:51–65.
MLA Yıldırım, İsa. “Strong and Weak Convergence of an Iterative Process for a Finite Family of Multivalued Mappings Satisfying the Condition (C)”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 1, 2017, pp. 51-65, doi:10.1501/Commua1_0000000774.
Vancouver Yıldırım İ. Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C). Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):51-65.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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