Variational principles and fixed point theorems

The paper concerns fundamental variational principles and the Caristi fixed point theorem. The Brézis–Browder theorem is extended and Altmanʼs theorem is investigated. The notion of istance, an extension of ω-distance, is defined. The new concept enables us to prove some elegant and general variational principles which imply a much stronger form of the Caristi and the Takahashi fixed point theorems. Another consequence is an advanced version of the Ekeland variational principle.