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    Quantum symmetric integral inequalities for convex functions
    (Wiley, 2024) Nosheen, Ammara; Ijaz, Sana; Khan, Khuram Ali; Awan, Khalid Mahmood; Budak, Hüseyin
    In the context of quantum symmetric calculus, this study proposed more refined version of Ostrowski and Hermite-Hadamard type inequalities. The function involved in these inequalities are convex functions. In order to reach the target, left and right quantum symmetric derivative and corresponding integral are used. Furthermore, the H & ouml;lder inequality is established in the frame work of left and right quantum symmetric integral. The new results refined the results about integral inequalities that exist in the literature.
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    Some extensions of Ostrowski type inequalities for q-symmetric integrals involving h-convex functions
    (Univ Nis, Fac Sci Math, 2024) Nosheen, Ammara; Khan, Khuram Ali; Ijaz, Sana; Budak, Huseyin
    This article presents the Ostrowski type inequalities for h-convex functions in the context of quantum variational calculus using the Montogmery identity involving q-symmetric integrals. Additionally, Holder's and Power mean inequalities involving q-symmetric integral are powerful tools to prove the results. Certain novel Ostrowski type inequalities for P-convex function, s-convex function, Godunova levin function, and s-Godunova Levin function are established, which are special instances of inequalities found for h-convex functions. Some examples are also provided along with graphical illusions to demonstrate the validity of the new discoveries. Our findings are regarded as generalizations of some known inequities from the literature.