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A NEW GENERALIZATION OF q-HERMITE-HADAMARD TYPE INTEGRAL INEQUALITIES FOR p, (p-s) AND MODIFIED (p-s)-CONVEX FUNCTIONS
(Element D.O.O., 2022) Gulshan, Ghazala; Hussain, R.; Budak, Hüseyin
In this study, we develop three new quantum Hermite-Hadamard inequalities for the class of p, (p-s) and modified type ( p-s) -convex functions by utilizing left and right quantum integral. As special cases of these inequalities, we get known and new Hermite-Hadamard type inequality for modified type (p-s) -convex functions. The ideas and techniques of this article may be the starting point for further research in this field. © 2023 Rockefeller University Press. All rights reserved.
On new version of Hermite-Jensen-mercer inequalities for newly defined quantum integral
(University of Miskolc, 2023) Gulshan, G.; Budak, Hüseyin; Hussain, R.; Sadiq, A.; Kösem, P.
In current study, we establish some new quantum Hermite Hadamard-Jensen-Mercer type integral inequalities by way of recently newly defined integral. Then we investigate the connections between our results and those in earlier works. Furthermore, we present some examples which satisfied our main outcomes. We expect that this innovative way opens many avenues for interested researchers will reconcile discovering further quantum approximations of Hermite-Hadamard type variants for other classes of convex functions, and, additionally, to discover uses in the aforementioned scientific disciplines. © (2023) All Rights Reserved.