Abstract
In this manuscript, first we introduce some new condition, inspirit of Suzuki’s (C)-condition, on a self-mapping T on a subset K of a Banach space E. Secondly, we obtain some new fixed point theorems under these conditions.
Keywords
- Inspirit
- Banach Sequence Space
- Fixed Point Theorem
- Banach Contraction Mapping Principle
- Quasi-nonexpansive Mappings
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abdeljawad T, Karapınar E (2009) Quasi-cone metric spaces and generalizations of Caristi Kirk’s theorem. Fixed Point Theory Appl 2009:9. Article ID 574387. doi:10.1155/ 2009/574387
Abdeljawad T, Karapınar E (2010) A gap in the paper “A note on cone metric fixed point theory and its equivalence”. [Nonlinear Anal 72(5):2259–2261]. Gazi Univ J Sci 24(2), 233–234 (2011)
Abdeljawad T, Karapınar E (2011) A common fixed point theorem of a Gregus type on convex cone metric spaces. J Comput Anal Appl 13(4):609–621
Banach S (1922) Surles operations dans les ensembles abstraits et leur application aux equations itegrales. Fund Math 3:133–181
Chatterjea SK (1972) Fixed-point theorems. C R Acad Bulgare Sci 25:727–730
Ćirić LB (1974) A generalization of Banach principle. Proc Am Math Soc 45:267–273
Edelstein M (1962) On fixed and periodic points under contractive mappings. J Lond Math Soc 37:74–79
Hardy GE, Rogers TD (1973) A generalization of a fixed point theorem of Reich. Canad Math Bull 16:201–206
Kannan R (1968) Some results on fixed points. Bull Cal Math Soc 60:71–76
Karapınar E (2009) Fixed point theorems in cone Banach spaces. Fixed Point Theory Appl 2009:9. Article ID 609281. doi:10.1155/2009/609281
Karapınar E (2010) Couple fixed point theorems for nonlinear contractions in cone metric spaces. Comput Math Appl 59(12):3656–3668. doi:10.1016/j.camwa.2010.03.062 (SCI)
Karapınar E (2010) Some fixed point theorems on the cone Banach spaces. In: Proceedings of 7th ISAAC congress, World Scientific, Singapore/Hackensack/London, pp 606–612
Karapınar E (2010) Some nonunique fixed point theorems of Ćirić type on cone metric spaces. Abstr Appl Anal 2010:14. Article ID 123094. doi:10.1155/2010/123094
Karapınar E (2011) Couple fixed point on cone metric spaces. Gazi Univ J Sci 21(1):51–58
Karapınar E (2011) Fixed point theory for cyclic weak-ϕ-contraction. Appl Math Lett 24(6):822–825. doi:10.1016/j.aml.2010.12.016
Karapınar E (2011) Weak ϕ-contraction on partial contraction and existence of fixed points in partially ordered sets, Mathematica Aeterna 1(4):237–244
Karapınar E, Türkolu DA (2010) Best approximations theorem for a couple in cone Banach space. Fixed Point Theory Appl 2010:9. Article ID 784578
Karapınar E, Yüksel U (2011) On common fixed point theorems without commuting conditions in tvs-cone metric spaces. J Comput Anal Appl 13(6):1115–1122
Reich S (1971) Kannan’s fixed point theorem. Boll Un Mat. Ital 4(4):1–11
Suzuki K (2008) A generalized Banach contraction principle that characterizes metric completeness. Proc Am Math Soc 136:1861–1869
Suzuki K (2008) Fixed point theorems and convergence theorems for some generalized non expansive mappings. J Math Anal Appl 340:1088–1095
Suzuki K (2009) A new type of fixed point theorem in metric spaces. Nonlinear Anal Theory Methods Appl 71(11):5313–5317
Opial Z (1967) Weak convergence of the sequence of successive approximation for nonexpansive mappings. Bull Am Math Soc 73:591–597
Singh SL, Mishra SN (2010) Remarks on recent fixed point theorems. Fixed Point Theory Appl 2010:18. Article ID 452905. doi:10.1155/2010/452905
Acknowledgments
I would like to thank to Professor Dimitru BALENAU who encouraged and supported me to attend NSC2010.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Karapinar, E. (2012). Remarks on Suzuki (C)-Condition. In: Luo, A., Machado, J., Baleanu, D. (eds) Dynamical Systems and Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0454-5_12
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0454-5_12
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0453-8
Online ISBN: 978-1-4614-0454-5
eBook Packages: EngineeringEngineering (R0)