Weakly Picard operators and applications. (English) Zbl 1035.47044
This article is a small survey of the author’s and other mathematicians’ results related to weakly Picard operators in a metric space \((X,d)\) (an operator \(A:X\to X\) is a weakly Picard one if the sequence \((A^nx)\) is convergent for any \(x\in X\) and its limit is a fixed ponit of \(A)\). Applications to differential, integral, and difference equations are also considered. Some open problems are formulated.
Reviewer: Peter Zabreiko (Minsk)
MSC:
47H10 | Fixed-point theorems |
47N20 | Applications of operator theory to differential and integral equations |
35J65 | Nonlinear boundary value problems for linear elliptic equations |
45N05 | Abstract integral equations, integral equations in abstract spaces |