Establishes conditions for functional inequalities related to generalized quasi-arithmetic means, implying broader applications in analysis.
The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider Hölder-, Minkowski-, and Jensen-type inequalities. Generalized quasi-arithmetic means are defined by taking strictly monotone generating functions instead of strictly monotone and continuous ones.
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Páles et al. (2026) studied this question.