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Suzuki, Tomonari

Fixed-point theorem for asymptotic contractions of Meir–Keeler type in complete metric spaces. (English) Zbl 1101.54047

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 5, 971-978 (2006).
Motivated essentially by the work of W. A. Kirk [J. Math. Anal. Appl. 277, No. 2, 645–650 (2003; Zbl 1022.47036)] and T.-C. Lim [Nonlinear Anal., Theory Methods Appl. 46, No. 1(A), 113–120 (2001; Zbl 1009.54044)], the author introduces the concept of asymptotic contraction of Meir-Keeler (\(ACMK\)) type on a metric space and obtains fixed point theorems fo such maps. The main result states that if \(T\) is an \(ACMK\) on a complete metric space \(X\) and if \(T^l\) is continuous for some natural number \(l\), then \(T\) has a unique fixed point.
Reviewer: S. L. Singh (Rishikesh)

Cited in 2 Reviews
Cited in 40 Documents

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems

Keywords:

Fixed point; Meir-Keeler contraction; asymptotic contraction of Meir-Keeler type

Citations:

Zbl 1022.47036; Zbl 1009.54044
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\textit{T. Suzuki}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 64, No. 5, 971--978 (2006; Zbl 1101.54047)
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References:

[1] Arandelović, I.D., On a fixed point theorem of kirk, J. math. anal. appl., 301, 384-385, (2005) · Zbl 1075.47031
[2] Banach, S., Sur LES opérations dans LES ensembles abstraits et leur application aux équations intégrales, Fund. math., 3, 133-181, (1922) · JFM 48.0201.01
[3] Boyd, D.W.; Wong, J.S.W., On nonlinear contractions, Proc. amer. math. soc., 20, 458-464, (1969) · Zbl 0175.44903
[4] Jachymski, J.R.; Jóźwik, I., On Kirk’s asymptotic contractions, J. math. anal. appl., 300, 147-159, (2004) · Zbl 1064.47052
[5] Kirk, W.A., Fixed points of asymptotic contractions, J. math. anal. appl., 277, 645-650, (2003) · Zbl 1022.47036
[6] Lim, T.C., On characterizations of meir – keeler contractive maps, Nonlinear anal., 46, 113-120, (2001) · Zbl 1009.54044
[7] Meir, A.; Keeler, E., A theorem on contraction mappings, J. math. anal. appl., 28, 326-329, (1969) · Zbl 0194.44904
[8] Suzuki, T., Several fixed point theorems in complete metric spaces, Yokohama math. J., 44, 61-72, (1997) · Zbl 0882.47039
[9] Suzuki, T., Several fixed point theorems concerning \(\tau\)-distance, Fixed point theory appl., 2004, 195-209, (2004) · Zbl 1076.54532
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