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A fixed point theorem for the sum of two mappings


Author: Olga Hadžić
Journal: Proc. Amer. Math. Soc. 85 (1982), 37-41
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1982-0647893-X
MathSciNet review: 647893
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Abstract: A generalization of a fixed point theorem of Rzepecki is proved and it is shown that in a paranormed space $ E$ this result yields, under certain circumstances, solutions to the equation $ x = Tx + Sx$ for $ T:E \to E$ either continuous and affine or a generalized contraction, and $ S:K \subseteq E \to E$ compact.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0647893-X
Keywords: Fixed point, paranormed space, $ \Phi $ paranormed space, generalized contraction
Article copyright: © Copyright 1982 American Mathematical Society

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