Sekin, CaglaTamar, Mehmet EminAliyev, Ilham A.2025-09-252025-09-2520231303-5991https://doi.org/10.31801/cfsuasmas.1262668https://search.trdizin.gov.tr/en/yayin/detay/1212479/new-proofs-of-fejers-and-discrete-hermite-hadamard-inequalities-with-applicationshttps://hdl.handle.net/20.500.12573/4281New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions f : [a, b] -> R about the midpoint c = (a+b)/2 are obtained and the reverse Hardy inequality for convex functions f : (0, infinity) -> (0, infinity) is established.eninfo:eu-repo/semantics/openAccessFejer InequalityConvex FunctionsDiscrete Hermite-Hadamard InequalityJensen InequalityHardy InequalityArticle10.31801/cfsuasmas.1262668