| Summary: | This paper establishes several new inequalities of Hermite–Hadamard type for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo></mrow><msup><mi>f</mi><mo>′</mo></msup><msup><mrow><mo>|</mo></mrow><mi>q</mi></msup></mrow></semantics></math></inline-formula> being convex for some fixed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>. As application, some error estimates on special means of real numbers are given.
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