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Abstract The purpose of this study is to demonstrate results on fixed point theory in quasi-partial b-metric space recognizing a new type of mapping, which is a blend of F-contraction and Kannan contraction, and to establish the fixed point results in F-expanding type mappings. Additionally, the obtained results are the application of the contractive mappings to functional equations. Furthermore, Mathematica software is used to demonstrate the 3D shapes of the examples discussed here.