The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces

Roughly speaking, Ekeland’s Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324–353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space. Later, Pando Georgiev (J. Math. Anal. Appl. 131 (1988), no. 1, 1–...
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Autor*in:	Ştefan Cobzaş [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	quasi-metric space completeness in quasi-metric spaces variational principles Ekeland variational principle strong Ekeland principle

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 12(2024), 3, p 471
Übergeordnetes Werk:	volume:12 ; year:2024 ; number:3, p 471

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math12030471

Katalog-ID:	DOAJ094483612

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spelling	10.3390/math12030471 doi (DE-627)DOAJ094483612 (DE-599)DOAJe1de81d61d6744ac95535aa051108f8b DE-627 ger DE-627 rakwb eng QA1-939 Ştefan Cobzaş verfasserin aut The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Roughly speaking, Ekeland’s Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324–353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space. Later, Pando Georgiev (J. Math. Anal. Appl. 131 (1988), no. 1, 1–21) and Tomonari Suzuki (J. Math. Anal. Appl. 320 (2006), no. 2, 787–794 and Nonlinear Anal. 72 (2010), no. 5, 2204–2209)) proved a Strong Ekeland Variational Principle, meaning the existence of strong minima for such perturbations. Please note that Suzuki also considered the case of functions defined on Banach spaces, emphasizing the key role played by reflexivity. In recent years, an increasing interest was manifested by many researchers to extend EkVP to the asymmetric case, i.e., to quasi-metric spaces (see references). Applications to optimization, behavioral sciences, and others were obtained. The aim of the present paper is to extend the strong Ekeland principle, both Georgiev’s and Suzuki’s versions, to the quasi-pseudometric case. At the end, we ask for the possibility of extending it to asymmetric normed spaces (i.e., the extension of Suzuki’s results). quasi-metric space completeness in quasi-metric spaces variational principles Ekeland variational principle strong Ekeland principle Mathematics In Mathematics MDPI AG, 2013 12(2024), 3, p 471 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:12 year:2024 number:3, p 471 https://doi.org/10.3390/math12030471 kostenfrei https://doaj.org/article/e1de81d61d6744ac95535aa051108f8b kostenfrei https://www.mdpi.com/2227-7390/12/3/471 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2024 3, p 471
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author	Ştefan Cobzaş
spellingShingle	Ştefan Cobzaş misc QA1-939 misc quasi-metric space misc completeness in quasi-metric spaces misc variational principles misc Ekeland variational principle misc strong Ekeland principle misc Mathematics The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces
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topic_title	QA1-939 The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces quasi-metric space completeness in quasi-metric spaces variational principles Ekeland variational principle strong Ekeland principle
topic	misc QA1-939 misc quasi-metric space misc completeness in quasi-metric spaces misc variational principles misc Ekeland variational principle misc strong Ekeland principle misc Mathematics
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title	The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces
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title_auth	The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces
abstract	Roughly speaking, Ekeland’s Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324–353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space. Later, Pando Georgiev (J. Math. Anal. Appl. 131 (1988), no. 1, 1–21) and Tomonari Suzuki (J. Math. Anal. Appl. 320 (2006), no. 2, 787–794 and Nonlinear Anal. 72 (2010), no. 5, 2204–2209)) proved a Strong Ekeland Variational Principle, meaning the existence of strong minima for such perturbations. Please note that Suzuki also considered the case of functions defined on Banach spaces, emphasizing the key role played by reflexivity. In recent years, an increasing interest was manifested by many researchers to extend EkVP to the asymmetric case, i.e., to quasi-metric spaces (see references). Applications to optimization, behavioral sciences, and others were obtained. The aim of the present paper is to extend the strong Ekeland principle, both Georgiev’s and Suzuki’s versions, to the quasi-pseudometric case. At the end, we ask for the possibility of extending it to asymmetric normed spaces (i.e., the extension of Suzuki’s results).
abstractGer	Roughly speaking, Ekeland’s Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324–353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space. Later, Pando Georgiev (J. Math. Anal. Appl. 131 (1988), no. 1, 1–21) and Tomonari Suzuki (J. Math. Anal. Appl. 320 (2006), no. 2, 787–794 and Nonlinear Anal. 72 (2010), no. 5, 2204–2209)) proved a Strong Ekeland Variational Principle, meaning the existence of strong minima for such perturbations. Please note that Suzuki also considered the case of functions defined on Banach spaces, emphasizing the key role played by reflexivity. In recent years, an increasing interest was manifested by many researchers to extend EkVP to the asymmetric case, i.e., to quasi-metric spaces (see references). Applications to optimization, behavioral sciences, and others were obtained. The aim of the present paper is to extend the strong Ekeland principle, both Georgiev’s and Suzuki’s versions, to the quasi-pseudometric case. At the end, we ask for the possibility of extending it to asymmetric normed spaces (i.e., the extension of Suzuki’s results).
abstract_unstemmed	Roughly speaking, Ekeland’s Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324–353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space. Later, Pando Georgiev (J. Math. Anal. Appl. 131 (1988), no. 1, 1–21) and Tomonari Suzuki (J. Math. Anal. Appl. 320 (2006), no. 2, 787–794 and Nonlinear Anal. 72 (2010), no. 5, 2204–2209)) proved a Strong Ekeland Variational Principle, meaning the existence of strong minima for such perturbations. Please note that Suzuki also considered the case of functions defined on Banach spaces, emphasizing the key role played by reflexivity. In recent years, an increasing interest was manifested by many researchers to extend EkVP to the asymmetric case, i.e., to quasi-metric spaces (see references). Applications to optimization, behavioral sciences, and others were obtained. The aim of the present paper is to extend the strong Ekeland principle, both Georgiev’s and Suzuki’s versions, to the quasi-pseudometric case. At the end, we ask for the possibility of extending it to asymmetric normed spaces (i.e., the extension of Suzuki’s results).
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