Fixed Point Theory in Banach Algebras

Afif Ben Amar and Donal O’Regan
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Afif Ben Amar: University of Sfax, Faculty of Sciences, Department of Mathematics
Donal O’Regan: National University of Ireland, Galway, School of Mathematics

Chapter Chapter 5 in Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications, 2016, pp 103-146 from Springer

Abstract: Abstract In this chapter we discuss x = A x B x + C x $$\displaystyle{ x = AxBx + Cx }$$ in suitable Banach algebras. We present some fixed point theory in Banach spaces under a weak topology setting. One difficulty that arises is that in a Banach algebra equipped with its weak topology the product of two weakly convergent sequences is not necessarily weakly convergent.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31948-3_5

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DOI: 10.1007/978-3-319-31948-3_5

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