Abstract
In this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for (gamma ,psi ,varphi ,phi ) contractions, rational-(gamma , psi ,varphi ,phi ) contractions and almost-(gamma ,psi , varphi ,phi ) contractions and φ-fixed disc results for (psi ,varphi ,phi )_{x_{0}} type 1 contractions, (psi ,varphi ,phi )_{x_{0}} type 2 contractions, and (psi ,varphi ,phi )_{x_{0}} type 3 contractions in metric spaces. We generalize some existing φ-fixed point and φ-fixed circle results in the literature. Further, we give some examples to demonstrate the usefulness of our results and investigate the existence and uniqueness of solutions of nonlinear integral equations.
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