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- W2977556055 abstract "Abstract We establish new quantum Hermite–Hadamard and midpoint types inequalities via a parameter $mu in [0,1]$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>μ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:math> for a function F whose $|{}_{alpha }D_{q}F|^{u}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> <mml:msub> <mml:mrow /> <mml:mi>α</mml:mi> </mml:msub> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mi>F</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> </mml:msup> </mml:math> is η -quasiconvex on $[alpha ,beta ]$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>[</mml:mo> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>]</mml:mo> </mml:math> with $ugeq 1$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>u</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> </mml:math> . Results obtained in this paper generalize, sharpen, and extend some results in the literature. For example, see (Noor et al. in Appl. Math. Comput. 251:675–679, 2015; Alp et al. in J. King Saud Univ., Sci. 30:193–203, 2018) and (Kunt et al. in Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112:969–992, 2018). By choosing different values of μ , loads of novel estimates can be deduced. We also present some illustrative examples to show how some consequences of our results may be applied to derive more quantum inequalities." @default.
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- W2977556055 date "2019-10-07" @default.
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- W2977556055 title "New parameterized quantum integral inequalities via η-quasiconvexity" @default.
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- W2977556055 doi "https://doi.org/10.1186/s13662-019-2358-z" @default.
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