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    A new version of q-Hermite-Hadamard's midpoint and trapezoid type inequalities for convex functions
    (Walter De Gruyter Gmbh, 2023) Ali, Muhammad Aamir; Budak, Hüseyin; Feckan, Michal; Khan, Sundas
    In this paper, we establish a new variant of q-Hermite-Hadamard inequality for convex functions via left and right q-integrals. Moreover, we prove some new q-midpoint and q-trapezoid type inequalities for left and right q-differentiable functions. To illustrate the newly established inequalities, we give some particular examples of convex functions.
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    On fractional Simpson type integral inequalities for co-ordinated convex functions
    (Springer, 2022) Khan, Sundas; Budak, Hüseyin
    In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using the established identity, we offer some Simpson's type inequalities for partially differentiable co-ordinated convex functions in a rectangle from the plane R-2.
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    ON MIDPOINT AND TRAPEZOID TYPE INEQUALITIES FOR MULTIPLICATIVE INTEGRALS
    (Publishing House of the Romanian Academy, 2022) Khan, Sundas; Budak, Hüseyin
    The purpose of this paper is to establish some Hermite-Hadamard type inequalities for multiplicative convex functions. First, we obtain two equal-ity for? differentiable functions. Then using these inequalities and multiplicative convex functions, we establish some inequalities related to the right and left hand side of Hermite-Hadamard inequality for multiplicative integrals. © 2022, Publishing House of the Romanian Academy. All rights reserved.
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    On new trapezoid and midpoint type inequalities for generalized quantum integrals
    (Univ Nis, Fac Sci Math, 2024) Budak, Hüseyin; Kara, Hasan; Tunc, Tuba; Hezenci, Fatih; Khan, Sundas
    In this article, by utilizing the functions with bounded second derivatives, we first prove some trapezoid and midpoint type inequalities for generalized quantum integrals which are introduced in the recent papers. Then we establish some new quantum integral inequalities for mappings whose second quantum derivatives are bounded. Moreover, we obtain some new weighted trapezoid and midpoint type inequalities for generalized quantum integrals by using the functions with bounded second derivatives. Finally, we investigate the connections between our results and those in earlier works.
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    Refinements of quantum Hermite-Hadamard- type inequalities
    (De Gruyter Poland Sp Z O O, 2021) Budak, Hüseyin; Khan, Sundas; Ali, Muhammad Aamir; Chu, Yu-Ming
    In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities.