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Phi-stable operators and inner approximation-solvability

Author: Ram U. Verma
Journal: Proc. Amer. Math. Soc. 117 (1993), 491-499
MSC: Primary 47H17; Secondary 47H09, 65J15
MathSciNet review: 1127144
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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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