Set-Valued Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle

Zhang Shi-sheng; Luo Qun

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Zhang Shi-sheng, Luo Qun. Set-Valued Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle[J]. Applied Mathematics and Mechanics, 1989, 10(2): 111-113.

Citation:

Zhang Shi-sheng, Luo Qun. Set-Valued Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle[J]. Applied Mathematics and Mechanics, 1989, 10(2): 111-113.

Citation:

Zhang Shi-sheng, Luo Qun. Set-Valued Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle[J]. Applied Mathematics and Mechanics, 1989, 10(2): 111-113.

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Set-Valued Caristi’s Fixed Point Theorem and Ekeland’s Variational Principle

Zhang Shi-sheng¹,
Luo Qun²

1.
Sichuan University, Chengdu;
2.
Guizhou Normal University, Guiyang

Received Date: 1987-11-02
Publish Date: 1989-02-15

Abstract

Abstract

This paper proposes a formally stronger set-valued Caristi's fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland's variational principle and thin set-valued Caristi's fixed point theorem. The results stated in this paper improve and strengthen the corresponding results in [4].

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References(4)

References

[1]	Ekeland,I.,On the variational principle,J.Math.Anal.Appl.,47(1974),324-353.
[2]	Ekeland,I.,Nonconvex minimization problems,Bull:Amer.Math.Soc.(New Series),1(1979),443-474.
[3]	Caristi,J.,Fixed point theorems for mappings satisfying inwardness conditions,Trans.Amer.Math.Soc.,215(1976),241-251.
[4]	史树中.Ekeland变分原理与Caristi不动点定理的等价性,数学进展,16,2 (1987), 203-206.