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New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations. (English) Zbl 1209.47026

The first part of the paper proposes fixed point theorems in Banach algebras for the following abstract fixed point equation involving three operators
\[ x=AxBx+Cx. \]
Then, in the second part some applications to two nonlinear functional integral equations in a suitable Banach algebra are given.

MSC:

47H10 Fixed-point theorems
45G10 Other nonlinear integral equations
47N20 Applications of operator theory to differential and integral equations
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