Ali, Muhammad AamirAbbas, MujahidBudak, HuseyinAgarwal, PraveenMurtaza, GhulamChu, Yu-Ming2021-12-012021-12-0120211687-1847https://doi.org/10.1186/s13662-021-03226-xhttps://hdl.handle.net/20.500.12684/10935In this research, we derive two generalized integral identities involving the q kappa 2-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson's and quantum Newton's inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson's and Newton's type inequalities by considering the limit q -> 1- in the key results of this paper.en10.1186/s13662-021-03226-xinfo:eu-repo/semantics/openAccessSimpson's <mml:mfrac><mml:mn>1</mml:mn><mml:mn>3</mml:mn></mml:mfrac> formulaSimpson's <mml:mfrac><mml:mn>3</mml:mn><mml:mn>8</mml:mn></mml:mfrac> formulaIntegral inequalitiesQuantum calculusPreinvex functionsArticle202112-s2.0-85099747063WOS:000613088800006N/AQ1