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In this paper, we introduce the notions of (F,ϕ,α-ψ)-contractions and (F,ϕ,α-ψ)-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness ϕ-fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature.

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