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

İsa Yıldırım

https://doi.org/10.1501/Commua1_0000000774

Cited By: 1

https://izlik.org/JA28AK24AF

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.