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A nonlinear alternative in Banach algebras with applications to functional differential equations. (English) Zbl 1067.47070

The author presents a new fixed point theorem, which he calls a nonlinear alternative of Dhage-Schaefer type. This theorem involves the product of two operators which act in a Banach algebra. An application to the solvability of the Cauchy problem for a first order nonlinear functional equation is given.

MSC:

47H10 Fixed-point theorems
34K40 Neutral functional-differential equations
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