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In this paper, by using the partial order method and monotone iterative techniques, the existence and uniqueness of fixed points for a class of superlinear operators are studied, without requiring any compactness or continuity. As corollaries, the new fixed point theorems for α-convex operators α>1, e-convex operators, positive α homogeneous operator α>1, generalized e-convex operator, and convex operators are obtained. The results are applied to nonlinear integral equations and partial differential equations.