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Abou Bakr, Sahar Mohamed Ali

Fixed point theorems of generalized contraction mappings on \(\varpi\)-cone metric spaces over Banach algebras. (English) Zbl 1502.54018

Rocky Mt. J. Math. 52, No. 3, 757-776 (2022).
Summary: Without the assumptions of normality and solidness, we investigate some properties of cones with some semiinterior points in normed algebras, introduce two novel notions of \(S\)-set and \(S\)-number associated with every semiinterior point in the underlying cone, give a constructive example with calculations of these new quantities, study some topological characterization of the topology induced by \(\varpi\)-cone metric of \(\varpi\)-cone metric space over Banach algebra with the help of semiinterior points instead of interior points, and then generalize some fixed point theorems of contraction type mapping defined on \(\varpi\)-cone metric space over Banach algebra with nonnormal and nonsolid cone.

Cited in 1 Review

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces

Keywords:

normal cones; solid cones; cone metric spaces over Banach algebras; \(b\)-cone metric spaces over Banach algebras; semiinterior points; fixed point theorems
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Full Text: DOI Link

References:

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