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    New Estimates for Hermite-Hadamard Inequality in Quantum Calculus via (alpha, m) Convexity
    (Mdpi, 2022) Xu, Peng; Butt, Saad Ihsan; Ul Ain, Qurat; Budak, Hüseyin
    This study provokes the existence of quantum Hermite-Hadamard inequalities under the concept of q-integral. We analyse and illustrate a new identity for the differentiable function mappings whose second derivatives in absolute value are (alpha, m) convex. Some basic inequalities such as Holder's and Power mean have been used to obtain new bounds and it has been determined that the main findings are generalizations of many results that exist in the literature. We make links between our findings and a number of well-known discoveries in the literature. The conclusion in this study unify and generalise previous findings on Hermite-Hadamard inequalities.
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    New quantum variants of Simpson-newton type inequalities via (?, m)-convexity
    (Kangwon-Kyungki Mathematical Soc, 2023) Butt, Saad Ihsan; Ul Ain, Qurat; Budak, Hüseyin
    . In this article, we will utilize (a, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using qe1-integral and qe1derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Holder's and Power mean, have been used to acquire new bounds.