Variational Principles and Fixed Points on Symmetric Structures

Mihai Turinici ()
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Mihai Turinici: A. I. Cuza University

A chapter in Geometry and Non-Convex Optimization, 2025, pp 789-831 from Springer

Abstract: Abstract 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.

Keywords: Ekeland variational principle; Symmetric space; Dependent choice principle; Convergent and Cauchy sequence; Caristi-Kirk theorem (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-3-031-87057-6_17

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