On I. Meghea and C. S. Stamin review article “Remarks on some variants of minimal point theorem and Ekeland variational principle with applications,” Demonstratio Mathematica 2022; 55: 354–379

• Autorzy: Göpfert Alfred , Tammer Christiane , Zălinescu Constantin

Identyfikatory

DOI

10.1515/dema-2023-0102

• Języki publikacji: EN

Abstrakty

EN

Being informed that one of our articles is cited in the paper mentioned in the title, we downloaded it, and we were surprised to see that, practically, all the results from our paper were reproduced in Section 3 of Meghea and Stamin’s article. Having in view the title of the article, one is tempted to think that the remarks mentioned in the paper are original and there are examples given as to where and how (at least) some of the reviewed results are effectively applied. Unfortunately, a closer look shows that most of those remarks in Section 3 are, in fact, extracted from our article, and it is not shown how a specific result is used in a certain application. So, our aim in the present note is to discuss the content of Section 3 of Meghea and Stamin’s paper, emphasizing their Remark 8, in which it is asserted that the proof of Lemma 7 in our article is “full of errors.”

Słowa kluczowe

EN

minimal point; Ekeland variational principle

PL

minimum funkcji; zasada wariacyjna Ekelanda

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20230102
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Göpfert Alfred

• Institute of Mathematics, University Halle-Wittenberg, D-06126 Halle, Germany

autor

Tammer Christiane

• Institute of Mathematics, University Halle-Wittenberg, D-06126 Halle, Germany

autor

Zălinescu Constantin

• Octav Mayer Institute of Mathematics, 700505-Iaşi, Romania

Bibliografia

• [1] I. Meghea and C. S. Stamin, Remarks on some variants of minimal point theorem and Ekeland variational principle with applications, Demonstr. Math. 55 (2022), 354–379.
• [2] A. Göpfert, Chr. Tammer, and C. Zălinescu, On the vectorial Ekeland’s variational principle and minimal points in product spaces, Nonlinear Anal. 39 (2000), 909–922.
• [3] A.B. Németh, A nonconvex vector minimization problem, Nonlinear Anal. 10 (1986), 669–678.
• [4] A.H. Hamel, Equivalents to Ekeland’s variational principle in uniform spaces, Nonlinear Anal. 62 (2005), 913–924.
• [5] A. Benbrik, A. Mbarki, S. Lahrech, and A. Ouahab, Ekeland’s principle for vector-valued maps based on the characterization of uniform spaces via families of generalized quasi-metrics, Lobachevskii J. Math. 21 (2006), 33–44.
• [6] Chr. Tammer, A generalization of Ekeland’s variational principle, Optimization 25 (1992), 129–141.
• [7] D.T. Luc, Theory of vector optimization, Lecture Notes in Economics and Mathematical Systems 319, Springer-Verlag, Berlin, 1989.
• [8] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324–353.
• [9] I. Meghea, On some perturbed variational principles: connexions and applications, Rev. Roumaine Math. Pures Appl. 54 (2009), 493–511.
• [10] I. Meghea, Ekeland variational principle: With generalizations and variants, Old City Publishing, Philadelphia, PA; Éditions des Archives Contemporaires, Paris, 2009.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).