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arXiv · 1902.09743

Ekeland, Takahashi and Caristi principles in quasi-pseudometric spaces

S. Cobzaş
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Abstract

We prove versions of Ekeland, Takahashi and Caristi principles in sequentially right $K$-complete quasi-pseudometric spaces (meaning asymmetric pseudometric spaces), the equivalence between these principles, as well as their equivalence to the completeness of the underlying quasi-pseudometric space. The key tools are Picard sequences for some special set-valued mappings corresponding to a function $φ$ on a quasi-pseudometric space, allowing a unitary treatment of all these principles.

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S. Cobzaş. 2019-03-09. Ekeland, Takahashi and Caristi principles in quasi-pseudometric spaces. https://arxiv.org/abs/1902.09743

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