We give the concept of multiplicative partial metric space, multiplicative metric-like space, multiplicative b-metric space and multiplicative b-metric-like space. Then we build the existence and uniqueness of fixed points in a multiplicative b-metric-like space as well as in a partially ordered multiplicative b-metric-like space. We derive some fixed point results in multiplicative partial metric spaces, multiplicative metric-like spaces and multiplicative b-metric spaces as an application, some examples and an application to existence of solution of integral equations.
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