
Journal of Convex Analysis 29 (2022), No. 1, 231242 Copyright Heldermann Verlag 2022 GMajorization and Fejér and HermiteHadamard Like Inequalities for GSymmetrized Convex Functions Marek Niezgoda Institute of Mathematics, Pedagogical University of Cracow, Cracow, Poland marek.niezgoda@up.krakow.pl For a given finite group G acting on an inner product space V, we introduce Gsymmetrized convex functions and Gsymmetrized increasing functions. We use them to establish some inequalities of Fejér and HermiteHadamard types. In particular, we apply Wright convexity. We interpret the obtained results for the group G = C_{n} of sign changes on V = R^{n}. The case n = 1 leads to some recent results by S. S. Dragomir [Symmetrized convexity and HermiteHadamard type inequalities, J. Math. Inequalities 10/4 (2016) 901918] and S. Abramovich and L.E. Persson [Some new HermiteHadamard and Fejer type inequalities without convexity/concavity, Math. Inequalities Appl. 23/2 (2020) 447458]. Keywords: Fejer inequality, HermiteHadamard inequality, Gmajorization, Gincreaasing function, convex function, Wright convex function, Gsymmetrized convex function, Gsymmetrized increasing monotone function. MSC: 52A41, 26D15; 26B25, 52A40. [ Fulltextpdf (106 KB)] for subscribers only. 