Phi-stable operators and inner approximation-solvability

Verma, Ram U.

doi:10.1090/S0002-9939-1993-1127144-X

Phi-stable operators and inner approximation-solvability
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by Ram U. Verma

Proc. Amer. Math. Soc. 117 (1993), 491-499

DOI: https://doi.org/10.1090/S0002-9939-1993-1127144-X

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Abstract:

We extend, by applying a theorem of Petryshyn (1970), the approximation-solvability of the nonlinear functional equations involving strongly stable Hilbert space mappings to the case of strongly $\phi$-stable mappings—a new and rather general class of mappings. These mappings constitute a generalization of monotone mappings. Finally, we upgrade the obtained results to the case of Banach space mappings.

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