10.30495/maca.2021.1929965.1011

A new version of the Hahn-Banach theorem in b-Banach spaces

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  • Mohammad Reza Haddadi1,
  • Hossein Alaeidizaji2,
  • Vahid Parvaneh3,
  1. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.
  2. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
  3. Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran.

Published in Issue 2021-06-21

How to Cite

A new version of the Hahn-Banach theorem in b-Banach spaces. (2021). Mathematical Analysis and Its Contemporary Applications, 3(3). https://doi.org/10.30495/maca.2021.1929965.1011

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Abstract

In this paper, we introduce the notion of b-Banach spaces and we present some examples. Also, we give an important extension of the Hahn-Banach theorem in a b-Banach space with an application.

Keywords

  • b-normed space,
  • b-Banach Space,
  • Hahn-Banach theorem
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References

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  2. S.R. Bernfeld, V. Lakshmikantham and Y.M. Reddy, Fixed point theorems of operators with PPF dependence in Banach spaces, Applicable Anal., 6(1977), 271-280.
  3. S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena., 46(2)(1998), 263-276.
  4. Kuratowski, K. Sur les espaces complets. Fund. Math., 15(1930), 301-309.