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Journal of Convex Analysis 29 (2022), No. 1, 231--242
Copyright Heldermann Verlag 2022

G-Majorization and FejÚr and Hermite-Hadamard Like Inequalities for G-Symmetrized Convex Functions

Marek Niezgoda
Institute of Mathematics, Pedagogical University of Cracow, Cracow, Poland

For a given finite group G acting on an inner product space V, we introduce G-symmetrized convex functions and G-symmetrized increasing functions. We use them to establish some inequalities of FejÚr and Hermite-Hadamard types. In particular, we apply Wright convexity. We interpret the obtained results for the group G = Cn of sign changes on V = Rn. The case n = 1 leads to some recent results by S. S. Dragomir [Symmetrized convexity and Hermite-Hadamard type inequalities, J. Math. Inequalities 10/4 (2016) 901--918] and S. Abramovich and L.-E. Persson [Some new Hermite-Hadamard and Fejer type inequalities without convexity/concavity, Math. Inequalities Appl. 23/2 (2020) 447--458].

Keywords: Fejer inequality, Hermite-Hadamard inequality, G-majorization, G-increaasing function, convex function, Wright convex function, G-symmetrized convex function, G-symmetrized increasing monotone function.

MSC: 52A41, 26D15; 26B25, 52A40.

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