Some new fixed point theorems under $$(\mathcal {A},\mathcal {S})$$ ( A , S ) -contractivity conditions

Abstract

In this manuscript we introduce a new class of contractivity conditions for mappings from a metric space into itself endowed with a binary relation (that is not necessarily a partial order). These conditions unify several kinds of contractive operators under some basic axioms, and they lead us to present some results about existence and uniqueness of fixed points that extend and generalize many theorems in the field of fixed point theory. One of the most attractive properties of this new class of operators is that they are not necessarily contractive, that is, there are non-contractive operators for which the presented results are applicable.