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A class of variational principles on symmetric structures is formulated, under the lines developed by Borwein and Preiss [Trans. Amer. Math. Soc., 303 (1987), 517–527]. The obtained results lie in the logical segment between dependent choice principle (DC) and Ekeland variational principle (EVP); so they are equivalent with both (DC) and (EVP). Then, as a by-product of these, some Caristi-Kirk principles over such structures are given, including a statement due to Bota et al. [Fixed Point Th., 12 (2011), 21–28], within the realm of Bakhtin metric spaces.

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Variational Principles and Fixed Points on Symmetric Structures

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  • 发表日期：

    2025年

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  • Mihai Turinici

摘要

A class of variational principles on symmetric structures is formulated, under the lines developed by Borwein and Preiss [Trans. Amer. Math. Soc., 303 (1987), 517–527]. The obtained results lie in the logical segment between dependent choice principle (DC) and Ekeland variational principle (EVP); so they are equivalent with both (DC) and (EVP). Then, as a by-product of these, some Caristi-Kirk principles over such structures are given, including a statement due to Bota et al. [Fixed Point Th., 12 (2011), 21–28], within the realm of Bakhtin metric spaces.