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The Journal of Analysis

, Volume 26, Issue 1, pp 49–59 | Cite as

Fixed point theorems for generalized multivalued contraction

Original Research Paper
First Online:
Received:
Accepted:
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Abstract

In this paper, a fixed point theorem for multi-valued mappings on a complete metric space is established taking a general contractive condition which generalizes several contractive conditions. Many generalizations of some well known results are also obtained as corollaries. Further, we give an application to the existence and uniqueness of solutions for certain classes of functional equations arising in dynamic programming.

Keywords

Multi-valued mapping Fixed points and generalized contraction 

Mathematics Subject Classification

47H10 54H25 
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Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This chapter does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

References

  1. 1.
    Bellman, R., and E.S. Lee. 1978. Functional equations arising in dynamic programming. Aequationes Mathematicae 17: 1–18.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Ćirić Lj, B. 1972. Fixed point for generalized multivalued contractions. Matematicki Vesnik 9 (24): 265–272.MathSciNetGoogle Scholar
  3. 3.
    Chatterjea, S.K. 1972. Fixed point theorems. Comptes rendus de l’Academie bulgare des Sciences 25: 727–730.MATHGoogle Scholar
  4. 4.
    Damjanović, B., and D. Đorić. 2011. Multivalued generalizations of the kannan fixed point theorem. Filomat 25: 125–131.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Đorić, D., and R. Lazović. 2011. Some Suzuki type fixed point theorems for generalized multivalued mappings and applications. Fixed Point Theory and Applications 2011: 40.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Kikkawa, M., and T. Suzuki. 2008. Some similarity between contractions and Kannan mappings. Fixed Point Theory and Applications 2008: 649749.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Kikkawa, M., and T. Suzuki. 2008. Three fixed point theorems for generalized contractions with constants in complete metric spaces. Nonlinear Analysi TMA 69: 2942–2949.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Liu, Z., R.P. Agarwal, and S.M. Kang. 2004. On solvability of functional equationa and system of functional equations arising in dynamic programming. Journal of Mathematical Analysis and Applications 297: 111–130.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Nadler, S.B. 1969. Multivalued contraction mapping. Pacific Journal of Mathematics 30: 475–488.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Reich, S. 1972. Fixed points of contractive functions. Bollettino dell’Unione Matematica Italiana 5: 26–42.MathSciNetMATHGoogle Scholar
  11. 11.
    Singh, S.L., and S.N. Mishra. 2010. Coincidence theorems for certain classes of hybrid contractions. Fixed Point Theory and Applications 2010: 898109.MathSciNetMATHGoogle Scholar
  12. 12.
    Suzuki, T. 2008. A generalized Banach contraction principle that characterizes metric completeness. Proceedings of the American Mathematical Society 136: 1861–1869.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Forum D'Analystes, Chennai 2017

Authors and Affiliations

  1. 1.Department of Mathematics, D. S. B. CampusKumaun UniversityNainitalIndia

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