Fixed point theorems for mappings with a contractive iterate at a point

Author:
Janusz Matkowski

Journal:
Proc. Amer. Math. Soc. **62** (1977), 344-348

MSC:
Primary 54H25

DOI:
https://doi.org/10.1090/S0002-9939-1977-0436113-5

MathSciNet review:
0436113

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Abstract | References | Similar Articles | Additional Information

Abstract: Let (*X,d*) be a complete metric space, , and be nondecreasing with respect to each variable. Suppose that for the function , the sequence of iterates tends to 0 in and . Furthermore, suppose that for each there exists a positive integer such that for all ,

*T*has a unique fixed point. This generalizes an earlier result of V. M. Sehgal and some recent results of L. Khazanchi and K. Iseki.

**[1]**L. F. Guseman,*Fixed point theorems for mappings with a contractive iterate at a point*, Proc. Amer. Math. Soc.**26**(1970), 615-618. MR**42**#919. MR**0266010 (42:919)****[2]**K. Iseki,*A generalization of Sehgal-Khazanchi's fixed point theorems*, Math. Seminar Notes Kobe Univ.**2**(1974), 1-9. MR**0436108 (55:9058)****[3]**L. Khazanchi,*Results on fixed points in complete metric space*, Math. Japonicae (to appear). MR**0400197 (53:4032)****[4]**V. M. Sehgal,*A fixed point theorem for mappings with a contractive iterate*, Proc. Amer. Math. Soc.**23**(1969), 631-634. MR**40**#3531. MR**0250292 (40:3531)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0436113-5

Keywords:
Fixed point,
orbit,
complete metric,
Cauchy sequence

Article copyright:
© Copyright 1977
American Mathematical Society