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    New symmetric midpoint type inequalities for convex functions
    (Univ Nis, Fac Sci Math, 2025) Hussain, Rashida; Gulshan, Ghazala; Rehman, Amara; Budak, Huseyin
    In this study, we first develop symmetric quantum integral identity utilizing the derivatives and integrals of symmetric quantum types. Then, by using this identity, we establish modified versions of midpoint-type inequalities for differentiable convex functions. To obtain recent results, a few basic inequalities such as power mean and Holder's, have been utilized. We create links between our results and previous findings in the literature taking q -> 1. For a better understanding and validation of the results, we present numerical results and some graphs. Finally, we provide some examples to illustrate the validity of newly obtained symmetric quantum inequalities. The concepts and methods presented in this work can inspire more investigation.
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    Symmetric midpoint-type inequalities for (α,m)-convex functions with applications
    (World Scientific Publ Co Pte Ltd, 2025) Hussain, Rashida; Gulshan, Ghazala; Rehman, Amara; Budak, Hueseyin
    In this study, we establish a modified version of the right symmetric quantum midpoint-type inequalities via (alpha, m)-convex differentiable functions with m is an element of [0, 1]. A few fundamental inequalities like Power mean and H & ouml;lder's have been applied to acquire recent results. The newly established findings can be changed into classical midpoint-type inequalities as well as q-midpoint-type inequalities for convex functions. Additionally, we provide an example and graph that support our main findings. It is supposed that these concepts and methods may encourage new analysis.