Fixed points for asymptotic contractions of integral Meir-Keeler type

Volume 5, Issue 2, pp 126--132 http://dx.doi.org/10.22436/jnsa.005.02.06

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Authors

Elisa Canzoneri - Dipartimento di Matematica e Informatica, Universita degli Studi di Palermo, Via Archirafi, 34--90123, Palermo, Italy. Pasquale Vetro - Dipartimento di Matematica e Informatica, Universita degli Studi di Palermo, Via Archirafi, 34 - 90123, Palermo, Italy.

Abstract

In this paper we introduce the notion of asymptotic contraction of integral Meir-Keeler type on a metric space and we prove a theorem which ensures existence and uniqueness of fixed points for such contractions. This result generalizes some recent results in the literature.

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Keywords

• Fixed points
• Asymptotic contractions of integral type
• Contractions of Meir-Keeler type.

MSC

•  47H10
•  54H25

References

• [1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. , 3 (1922), 133-181.


• [2] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. , 29 (2002), 531-536.


• [3] K. Goebel, W. A. Kirk, Topics in metric fixed-point theory , Cambridge Univ. Press, Cambridge (1990)


• [4] W. A. Kirk, B. G. Kang, A fixed point theorem revisited , J. Korean Math. Soc. , 34 (1997), 285-291.


• [5] W. A. Kirk, B. Sims, Handbook of metric fixed point theory, Kluwer Academic Publishers, Dordrecht (2001)


• [6] W. A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. , 277 (2003), 645-650.


• [7] A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. , 28 (1969), 326-329.


• [8] T. Suzuki , Meir-Keeler contractions of integral type are still Meir-Keeler contractions, Int. J. Math. Math. Sci., Article ID 39281, 2007 (2007), 6 pages.


• [9] T. Suzuki , Several fixed point theorems in complete metric spaces , Yokohama Math. J. , 44 (1997), 61-72.


• [10] T. Suzuki , Several fixed point theorems concerning-distance, Fixed Point Theory Appl. , 2004 (2004), 195-209.


• [11] T. Suzuki, Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Nonlinear Anal. , 64 (2006), 971-978.