Some results on the projective cone normed tensor product spaces over banach algebras

  • Dipankar Das Gauhati University Department of Mathematics
  • Nilakshi Goswami Gauhati University Department of Mathematics
  • Vishnu Narayan Mishra Indira Gandhi National Tribal University Department of Mathematics http://orcid.org/0000-0002-2159-7710

Resumo

For two real Banach algebras $\mathbb{A}_1$ and $\mathbb{A}_2$, let $K_p$ be the projective cone in $\mathbb{A}_1\otimes_\gamma \mathbb{A}_2$. Using this we define a cone norm on the algebraic tensor product of two vector spaces over the Banach algebra $\mathbb{A}_1\otimes_\gamma \mathbb{A}_2$ and discuss some properties. We derive some fixed point theorems in this projective cone normed tensor product space over Banach algebra with a suitable example. For two self mappings $S$ and $T$ on a cone Banach space over Banach algebra, the stability of the iteration scheme $x_{2n+1}=Sx_{2n}$, $x_{2n+2}=Tx_{2n+1},\;n=0,1,2,...$ converging to the common fixed point of $S$ and $T$ is also discussed here.

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Biografia do Autor

Vishnu Narayan Mishra, Indira Gandhi National Tribal University Department of Mathematics
Ichchhanath Mahadev Dumas Road, Surat (Gujarat), India, Pin Code : 395 007.
Publicado
2018-02-19
Seção
Artigos