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We extend the notion of (α ψ, β φ )-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.

Discussion on Generalized-(α ψ, β φ )-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems