In the article, we considered the fixed point problem for contractive mappings of integral type in the setting of $ b $-metric spaces for the first time. First, we introduced the concepts of $ \theta $-weak contraction and $ \theta $-$ \psi $-weak contraction. Second, the existence and uniqueness of fixed points of contractive mappings of integral type in $ b $-metric spaces were studied. Meanwhile, two examples were given to prove the feasibility of our results. As an application, we proved the solvability of a functional equation arising in dynamic programming.
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