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In this paper, some basic results under various conditions for φ-convex functions are investigated. We prove that, under special hypotheses, every φ-convex function f is continuous on (a, b). Moreover, we introduce the notion of (φ, n)-convex functions.doi:10.29252/maco.1.2.12 fatcat:rs64zrdogzbbrootxgxw6aacbm