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

Abstract

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.

Keywords

• Razumikhin class
• <i>PPF</i>-dependent fixed point
• <i>α</i>-admissible nonself-mapping
• <i>α</i>-<i>F</i>-contractive nonself-mapping
• weak <i>α</i>-<i>F</i>-contractive nonself-mapping
• generalized <i>α</i>-<i>F</i>-contractive nonself-mapping
• graph
• (partial) order