| Summary: | In this paper, we introduce the concepts of an <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-admissible nonself-mapping, an <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<i>F</i>-contractive nonself-mapping, a weak <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<i>F</i>-contractive nonself-mapping, and a generalized <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<i>F</i>-contractive nonself-mapping and prove some <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mi>P</mi> <mi>F</mi> </mrow> </semantics> </math> </inline-formula> (past-present-future)-dependent fixed point theorems for the proposed contractive nonself-mappings in certain Razumikhin classes. By using our results, we derive some <inline-formula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mi>P</mi> <mi>F</mi> </mrow> </semantics> </math> </inline-formula>-dependent fixed point theorems for an <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-<i>F</i>-contractive nonself-mapping endowed with a graph or a partial order. Finally, we give some applications to illustrate the main results.
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