A variant of Jensen–Steffensen's inequality and quasi-arithmetic means
Copyright policy )A variant of Jensen–Steffensen's inequality and quasi-arithmetic means
A variant of Jensen-Steffensen's inequality is proved. Necessary and sufficient conditions for the equality in Jensen-Steffensen's inequality are established. Several inequalities involving more than two monotonic functions and generalized quasi-arithmetic means with not only positive weights are proved. It is shown that such generalized quasi-arithmetic means have the same comparability properties as those with positive weights.
Monotonicity, quasi-arithmetic means, Jensen–Steffensen's inequality, Jensen-Steffensen's inequality; monotonicity; quasi-arithmetic means; power means, Applied Mathematics, Jensen-Steffensen's inequality, monotonicity, Power means, Quasi-arithmetic means, Inequalities for sums, series and integrals, Functional inequalities, including subadditivity, convexity, etc., power means, Jensen-Steffensen inequality, Analysis, Means
Monotonicity, quasi-arithmetic means, Jensen–Steffensen's inequality, Jensen-Steffensen's inequality; monotonicity; quasi-arithmetic means; power means, Applied Mathematics, Jensen-Steffensen's inequality, monotonicity, Power means, Quasi-arithmetic means, Inequalities for sums, series and integrals, Functional inequalities, including subadditivity, convexity, etc., power means, Jensen-Steffensen inequality, Analysis, Means
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