Some PPF Dependent Fixed Point Theorems for Generalized α - F -Contractions in Banach Spaces and Applications

摘要

In this paper, we introduce the concepts of an α -admissible nonself-mapping, an α - F -contractive nonself-mapping, a weak α - F -contractive nonself-mapping, and a generalized α - F -contractive nonself-mapping and prove some P P F (past-present-future)-dependent fixed point theorems for the proposed contractive nonself-mappings in certain Razumikhin classes. By using our results, we derive some P P F -dependent fixed point theorems for an α - F -contractive nonself-mapping endowed with a graph or a partial order. Finally, we give some applications to illustrate the main results.