Fixed Points of Demicontinuous φ-Nearly Lipschitzian Mappings in Banach Spaces

Godwin Amechi Okeke, Johnson O Olaleru

Abstract

In this study, we introduce the classes of φ-nearly contraction mappings, φ-nearly nonexpansive mappings, φ-nearly asymptotically nonexpansive mappings, φ-nearly uniformly k-Lipschitzian mappings and φ-nearly uniform kcontraction mappings. These classes include those classes studied by Sahu [1] as special cases. We study the existence of fixed points and the structure of their fixed point sets of mappings in Banach spaces. Our results improve and generalize many celebrated results of fixed point theory in the context of demicontinuity.