Abstract
By using the Jensen–Mercer inequality for strongly convex functions, we present Hermite–Hadamard–Mercer inequality for strongly convex functions. Furthermore, we also present some new Hermite‐Hadamard‐Mercer-type inequalities for differentiable functions whose derivatives in absolute value are convex.
Highlights
Mathematical inequalities play a vital role in many fields of science. e field of mathematical inequalities and applications has enrolled an exponential improvement in the last two decades with a significant impact in other fields of modern mathematics including engineering [1], mathematical statistics [2], approximation theory [3, 4], information theory [5], and other disciplines [6]
We derive some new inequalities related to the right and left sides of the Hermite–Hadamard–Mercer type inequalities for differentiable functions whose derivatives in the absolute value are convex
For obtaining the right side of (28), use the definition of strongly convex function, and we have a θ
Summary
Mathematical inequalities play a vital role in many fields of science. e field of mathematical inequalities and applications has enrolled an exponential improvement in the last two decades with a significant impact in other fields of modern mathematics including engineering [1], mathematical statistics [2], approximation theory [3, 4], information theory [5], and other disciplines [6]. X1 min1≤i≤nxi, Substitute n 2 in (6); we obtain Jensen–Mercer inequality for strongly convex functions as follows: θm + M −
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