Opial modulus, moduli of noncompact convexity and fixed points for asymptotically regular mappings
Let \(C\) be a nonempty closed bounded convex subset of a Banach space. A map \(T: C \rightarrow C\) is said to be asymptotically regular if \(\lim_n\|T^{n+1}x - T^nx\|= 0\) for every \(x \in C\). Sufficient conditions for the existence of fixed points of asymptotically regular maps are given in the terms of the weakly convergent sequence coefficient, the Opial's modulus and moduli of noncompact convexity.
scientific article; zbMATH DE number 1512498