In this paper, we introduce a new type of contractions on a metric space (X,d) in which the distance d(x,y) is replaced with a function, depending on a parameter λ, that is not symmetric in general. This function generalizes the usual case when λ=1/2 and can take bigger values than m1/2. We call these new types of contractions λ-weak contractions and we provide some of their properties. Moreover, we investigate cases when these contractions are Picard operators.

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