New proofs of Fejer's and discrete Hermite-Hadamard inequalities with applications

Authors : Çağla Sekin, Mehmet Emin Tamar, Ilham Aliyev

Pages : 1110-1125

Doi:10.31801/cfsuasmas.1262668

View : 78 | Download : 131

Publication Date : 2023-12-29

Article Type : Research Paper

Abstract :New 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 $f:[a,b]\\rightarrow \\mathbb{R}$ about the midpoint $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:(0,\\infty )\\rightarrow (0,\\infty )$ is established.
Keywords : Fejer inequality, convex functions, discrete Hermite Hadamard inequality, Jensen inequality, Hardy inequality