Fixed point theorems and demiclosedness principle for mappings of asymptotically nonexpansive type in Banach spaces

Abstract

In this article, we prove the existence of fixed points for the mappings of asymptotically non-expansive type in a Banach space with its characteristic of noncompact convexity associated to the separation measure of noncompactness less than the weakly convergent sequence coefficient. We also verify the demiclosedness principle for mappings of asymptotically nonexpansive type in Banach spaces with locally uniform Opial condition. Mathematics Subject Classification: 47H09; 47H10.