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

Dhage, B. C.

Nonlinear Funct. Anal. Appl. 9, No. 4, 563-575 (2004).

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.

Reviewer: Gheorghe Moroşanu (Budapest)

MSC:

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

Keywords:

fixed point theorem; Banach algebra; functional differential equation; solvability; Cauchy problem