functional equation

nonexpansive mappings

fixed point property

Proceedings of the American Mathematical Society

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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi"> <mml:semantics> <mml:mi>ϕ</mml:mi> <mml:annotation encoding="application/x-tex">\phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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.

Phi-stable operators and inner approximation-solvability