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Remarks on Suzuki (C)-Condition

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Dynamical Systems and Methods

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.

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References

  1. 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

    Google Scholar 

  2. 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)

    Google Scholar 

  3. 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

    MathSciNet  MATH  Google Scholar 

  4. Banach S (1922) Surles operations dans les ensembles abstraits et leur application aux equations itegrales. Fund Math 3:133–181

    MATH  Google Scholar 

  5. Chatterjea SK (1972) Fixed-point theorems. C R Acad Bulgare Sci 25:727–730

    MathSciNet  MATH  Google Scholar 

  6. Ćirić LB (1974) A generalization of Banach principle. Proc Am Math Soc 45:267–273

    MATH  Google Scholar 

  7. Edelstein M (1962) On fixed and periodic points under contractive mappings. J Lond Math Soc 37:74–79

    Article  MathSciNet  MATH  Google Scholar 

  8. Hardy GE, Rogers TD (1973) A generalization of a fixed point theorem of Reich. Canad Math Bull 16:201–206

    Article  MathSciNet  MATH  Google Scholar 

  9. Kannan R (1968) Some results on fixed points. Bull Cal Math Soc 60:71–76

    MATH  Google Scholar 

  10. Karapınar E (2009) Fixed point theorems in cone Banach spaces. Fixed Point Theory Appl 2009:9. Article ID 609281. doi:10.1155/2009/609281

    Google Scholar 

  11. 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)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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

    Google Scholar 

  13. 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

    Google Scholar 

  14. Karapınar E (2011) Couple fixed point on cone metric spaces. Gazi Univ J Sci 21(1):51–58

    Google Scholar 

  15. 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

    Article  MathSciNet  MATH  Google Scholar 

  16. Karapınar E (2011) Weak ϕ-contraction on partial contraction and existence of fixed points in partially ordered sets, Mathematica Aeterna 1(4):237–244

    MathSciNet  Google Scholar 

  17. Karapınar E, Türkolu DA (2010) Best approximations theorem for a couple in cone Banach space. Fixed Point Theory Appl 2010:9. Article ID 784578

    Google Scholar 

  18. 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

    MathSciNet  MATH  Google Scholar 

  19. Reich S (1971) Kannan’s fixed point theorem. Boll Un Mat. Ital 4(4):1–11

    MathSciNet  MATH  Google Scholar 

  20. Suzuki K (2008) A generalized Banach contraction principle that characterizes metric completeness. Proc Am Math Soc 136:1861–1869

    Article  MATH  Google Scholar 

  21. Suzuki K (2008) Fixed point theorems and convergence theorems for some generalized non expansive mappings. J Math Anal Appl 340:1088–1095

    Article  MathSciNet  MATH  Google Scholar 

  22. Suzuki K (2009) A new type of fixed point theorem in metric spaces. Nonlinear Anal Theory Methods Appl 71(11):5313–5317

    Article  MATH  Google Scholar 

  23. Opial Z (1967) Weak convergence of the sequence of successive approximation for nonexpansive mappings. Bull Am Math Soc 73:591–597

    Article  MathSciNet  MATH  Google Scholar 

  24. 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

    Google Scholar 

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Acknowledgments

I would like to thank to Professor Dimitru BALENAU who encouraged and supported me to attend NSC2010.

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Authors and Affiliations

  1. Department of Mathematics, Atılım University, 06836, Incek, Ankara, Turkey

    Erdal Karapinar

Authors
  1. Erdal Karapinar
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Correspondence to Erdal Karapinar .

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Editors and Affiliations

  1. Edwardsville, School of Engineering, Southern Illinois University, Room: EB2064, Edwardsville, 62026-1805, USA

    Albert C.J. Luo

  2. Institute of Engineering, Department of Electrical Engineering, Polytechnic Institute of Porto, Rua Dr António Bernadino Almeida 431, Porto, 4200-072, Portugal

    José António Tenreiro Machado

  3. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

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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

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  • DOI: https://doi.org/10.1007/978-1-4614-0454-5_12

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-0453-8

  • Online ISBN: 978-1-4614-0454-5

  • eBook Packages: EngineeringEngineering (R0)

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