a b s t r a c tDue to its possible applications, Fixed Point Theory has become one of the most useful branches of Nonlinear Analysis. In a very recent paper, Khojasteh et al. introduced the notion of simulation function in order to express different contractivity conditions in a unified way, and they obtained some fixed point results. In this paper, we slightly modify their notion of simulation function and we investigate the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions.

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In this paper, using the concept of ω -admissibility, we prove some fixed point results for interpolate Ćirić-Reich-Rus-type contraction mappings. We also present some consequences and a useful example.

We investigate the existence and uniqueness of a fixed point of an operator via simultaneous functions in the setting of complete quasi-metric spaces. Our results generalize and improve several recent results in literature.

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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.

In this manuscript we introduce the notions of R-function and R-contractions, and we show an ad hoc fixed point theorem. We prove that this new kind of contractions properly includes the family of all Meir-Keeler contractions and other well-known classes of contractions that have been given very recently (for instance, those using simulation functions and manageable functions). As a consequence, our approach turns out to be appropriate to unify the treatment of different kinds of contractive nonlinear operators.MSC: 46T99; 47H10; 47H09; 54H25

We extend the notion of ( , )-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts., ∈ : R ⇒ R .(1)