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Zbl 0897.54029
Kada, Osamu; Suzuki, Tomonari; Takahashi, Wataru
Nonconvex minimization theorems and fixed point theorems in complete metric spaces. (English)
[J] Math. Jap. 44, No.2, 381-391 (1996). ISSN 0025-5513

Let $(X,d)$ be a metric space. The authors first introduce the concept of $w$-distance, it is a generalization of metric $d$ on $X$. They establish some properties of $w$-distance and prove a nonconvex minimization theorem which improves a result of Takahashi. They also improve Caristi's fixed point theorem and Ekeland's $E$-variational principle. They also prove a fixed point theorem in a complete metric space and apply this theorem to prove Subrahmanyam's fixed point theorem, Kaman's fixed point theorem, and Čirič's fixed point theorem. The results of this paper seem useful, interesting, and original.
[L.-J.Lin (Changhua)]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
49J45 Optimal control problems inv. semicontinuity and convergence
49J40 Variational methods including variational inequalities

Keywords: $w$-distance; Ekeland's $E$-variational principle; Caristi's fixed point theorem

Cited in: Zbl 1230.54048 Zbl 1229.54057 Zbl pre06150142 Zbl 1236.49011 Zbl 1226.54051 Zbl 1204.54037 Zbl 1203.54050 Zbl 1188.54017 Zbl 1215.47095 Zbl 1171.54031 Zbl pre06160822 Zbl 1143.54018 Zbl 1212.49031 Zbl 1156.47307 Zbl 1121.47305 Zbl 1078.54025 Zbl 1020.47048 Zbl 1015.54022 Zbl 0981.54019 Zbl 0986.54015

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