A generalization of the Hahn-Banach theorem in seminormed quasilinear spaces

• Autorzy: Çakan Sümeyye , Yılmaz Yilmaz

Identyfikatory

DOI

10.7862/rf.2019.5

• Języki publikacji: EN

Abstrakty

EN

The concept of normed quasilinear spaces which is a generalization of normed linear spaces gives us a new opportunity to study with a similar approach to classical functional analysis. In this study, we introduce the notion of seminormed quasilinear space as a generalization of normed quasilinear spaces and give various auxiliary results and examples. We present an analog of Hahn-Banach theorem, in seminormed quasilinear spaces.

Słowa kluczowe

EN

quasilinear spaces; normed quasilinear spaces; seminormed quasilinear spaces; semimetrizable quasilinear spaces; Hahn-Banach theorem

PL

przestrzenie quasi-liniowe; przestrzenie quasi-unormowane; twierdzenie Hahna-Banacha

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2019
• Tom: Vol. 42
• Strony: 79--94
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Çakan Sümeyye

• Department of Mathematics, Inönü University, Malatya 44280, TURKEY

autor

Yılmaz Yilmaz

• Department of Mathematics, Inönü University, Malatya 44280, TURKEY

Bibliografia

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• [3] J.P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990.
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• [5] S. Çakan, Y. Yılmaz, Localization Principle in Normed Quasilinear Spaces, Information Sciences and Computing, Article ID ISC530515 (2015) 15 pages.
• [6] S. Çakan, Y. Yılmaz, Normed proper quasilinear spaces, J. Nonlinear Sci. Appl. 8 (2015) 816–836.
• [7] S. Çakan, Y. Yılmaz, On the quasimodules and normed quasimodules, Nonlinear Funct. Anal. Appl. 20 (2) (2015) 269–288.
• [8] S. Çakan, Y. Yılmaz, Lower and upper semi basis in quasilinear spaces, Erciyes University Journal of the Institute of Science and Technology 31 (2) (2015) 97–104.
• [9] S. Çakan, Y. Yılmaz, Lower and upper semi convergence in normed quasilinear spaces, Nonlinear Funct. Anal. Appl. 21 (3) (2016) 501–511.
• [10] V. Lakshmikantham, T.G. Bhaskar, J.V. Devi, Theory of Set Differential Equations in Metric Spaces, Cambridge Scientific Publishers, Cambridge, 2006.
• [11] R.E. Moore, R.B. Kearfott, M.J. Cloud, Introduction to Interval Analysis, SIAM, Philadelphia, USA, 2009.
• [12] Y. Yılmaz, S. Çakan, S¸. Aytekin, Topological quasilinear spaces, Abstr. Appl. Anal., Article ID 951374 (2012) 10 pages.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).