The paper proves a fixed point theorem for random asymptotically pointwise contractions in bounded random normed modules by applying a deterministic theorem in L^p(E) after choosing p large enough that 5^{1/p}λ < 1.
Banach, Sur les op´ erations dans les ensembles abstraits et leur applica- tion aux ´ equations int´ egrales,Fund
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A Fixed Point Theorem for Random Asymptotically Pointwise Contractions
The paper proves a fixed point theorem for random asymptotically pointwise contractions in bounded random normed modules by applying a deterministic theorem in L^p(E) after choosing p large enough that 5^{1/p}λ < 1.