Some Results on Uniformly Lipschitzian Mappings in Metric Spaces and ApplicationsA. Aghajani, A.M. Tehrani (pp. 194-201)
In this work, we obtain a useful property of uniformly Lipschitzian mappings, then we give some suitable conditions under which uniformly Lipschitzian mappings have a fixed point without limiting conditions on the Lipschitz constant L in metric spaces. As an application of our main results we investigate the solvability of Fredholm integral equations of second kind. Some illustrative examples are included to show the usefulness and applicability of results.
fixed-point theorems, uniformly Lipschitzian mappings, nonexpansive mappings, Fredholm integral equations.