(φ₁, φ₂)-Variational principle

2016/10/19 by Abdelhakim Maaden, Maaden, Abdelhakim, Abdelkader Stouti +1
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1610.05915

openalex publication_date 2016/10/19 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that if X is a Banach space, then for every lower semi-continuous bounded below function f, there exists a (φ₁, φ₂)-convex function g, with arbitrarily small norm, such that f + g attains its strong minimum on X. This result extends some of the well-known varitional principles as that of Ekeland [18], that of Borwein-Preiss [6] and that of Deville-Godefroy-Zizler [14, 15].

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