Abstract
The purpose of this paper is to introduce and study the strong convergence problem of the explicit iteration process for a Lipschitzian and demi-contraction semi-groups in arbitrary Banach spaces. The main results presented in this paper extend and improve some recent results announced by many authors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aleyner, A., Reich, S.: An explicit construction of sunny nonexpansive retractions in Banach spaces. Fixed Point Theory and Appl. 3, 295–305 (2005)
Shioji, N., Takahashi, W.: Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces. Nonliear Anal. 34, 87–99 (1998)
Suzuki, T.: On strong convergence to a common fixed point of nonexpansive semigroup in Hilbert spaces. Proc. Amer. Math. Soc. 131, 2133–2136 (2003)
Xu, H.K.: Astrong convergence theorem for contraction semigroups in Banach spaces. Bull. Austral. Math. Soc. 72, 371–379 (2005)
Xu, H.K.: Inequonualities in Banach spaces with applications. Nonliear Anal. 16, 1127–1138 (1991)
Chang, S.S., Yang, L., Liu, J.A.: Strong convergence theorem for nonexpansive semi-groups in Banach spaces. Appl. Math. Mech. 28, 1287–1297 (2007)
Zhang, S.S.: Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces. Appl. Math. Mech. 30, 145–152 (2009)
Zhang, S.S.: Weak convergence theorem for Lischitzian pseudo-contract semi-groups in Banach spaces. Acta Math. Sinica, Chinese Series 26, 337–344 (2010)
Li, S., Li, L.H., Su, F.: General iterative methods for a one-parameter nonexpansive semi-group in Hilbert space. Nonlinear Anal. (2008), doi:10.1016/j.na.2008.04.007
Osilike, M.O.: Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps. J. Math. Anal. Appl. 294, 73–81 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dingping, W. (2013). Strong Convergence Theorems for Lipschitzian Demi-Contraction Semigroups in Banach Spaces. In: Yang, G. (eds) Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering. Advances in Intelligent Systems and Computing, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31698-2_99
Download citation
DOI: https://doi.org/10.1007/978-3-642-31698-2_99
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31697-5
Online ISBN: 978-3-642-31698-2
eBook Packages: EngineeringEngineering (R0)