| Summary: | In this paper, we use <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>q</mi><mi>a</mi></msub></semantics></math></inline-formula>- and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>q</mi><mi>b</mi></msup></semantics></math></inline-formula>-integrals to establish some quantum Hermite–Hadamard–Fejér-type inequalities for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-convex functions. By taking <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>→</mo><mn>1</mn></mrow></semantics></math></inline-formula>, our results reduce to classical results on Hermite–Hadamard–Fejér-type inequalities for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-convex functions. Moreover, we give some examples for quantum Hermite–Hadamard–Fejér-type inequalities for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-convex functions. Some results presented here for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-convex functions provide extensions of others given in earlier works for convex and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-convex functions.
|
|---|