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arxiv: 1211.4599 · v1 · pith:DOTYJKM3new · submitted 2012-11-19 · 🧮 math.CA

On φ-convexity

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keywords varphiconvexitymidconvexityapproximatecalledcharacterizationsconvexestablished
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In this paper, approximate convexity and approximate midconvexity properties, called $\varphi$-convexity and $\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\varphi$-convex and $\varphi$-midconvex functions are obtained. Furthermore, the relationship between $\varphi$-midconvexity and $\varphi$-convexity is established.

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