Pólya type integral inequalities: Origin, variants, proofs, refinements, generalizations, equivalences, and applications

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• Feng Qi

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• Primary
• 26D15
• Secondary
• 33C75
• 33E05
• 41A55

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• Pólya's integral inequality
• Iyengar-Mahajani's integral inequality
• Agarwal-Cerone-Dragomir's integral inequality
• Qi's integral inequality
• equivalent relation
• Steffensen's inequality
• Hayashi's integral inequality
• Rolle's mean value theorem
• Lagrange's mean value theorem
• Taylor's mean value theorem with Lagrange's remainder
• convex function
• mean
• complete elliptic integral
• geometric proof
• analytic proof
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