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

In this study, we introduce the classes of phi-nearly contraction mappings, phi-nearly nonexpansive mappings, phi-nearly asymptotically nonexpansive mappings, phi-nearly uniformly k-Lipschitzian mappings and phi-nearly uniform k-contraction 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.