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    Generalized fractional integral inequalities for product of two convex functions
    (Forum Editrice Univ Udinese, 2021) Ali, Muhammad Aamir; Budak, Hüseyin; Sial, Ifra Bashir
    The aim of this paper is to generalize the results proved in [4] using generalized fractional integral. Some special cases are deduced from main results. Applying the techniques of our results, new results may be obtained during a similar manner for various operators.
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    On Some New Ostrowski-Mercer-Type Inequalities for Differentiable Functions
    (Mdpi, 2022) Sial, Ifra Bashir; Patanarapeelert, Nichaphat; Ali, Muhammad Aamir; Budak, Hüseyin; Sitthiwirattham, Thanin
    In this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some Ostrowski-Mercer-type inequalities for differentiable convex functions. It is also demonstrated that the newly established inequalities are generalizations of some of the Ostrowski inequalities established inside the literature. There are also some applications to the special means of real numbers given.
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    Post-quantum Ostrowski type integral inequalities for functions of two variables
    (Amer Inst Mathematical Sciences-Aims, 2022) Vivas-Cortez, Miguel J. J.; Ali, Muhammad Aamir; Budak, Hüseyin; Sial, Ifra Bashir
    In this study, we give the notions about some new post-quantum partial derivatives and then use these derivatives to prove an integral equality via post-quantum double integrals. We establish some new post-quantum Ostrowski type inequalities for differentiable coordinated functions using the newly established equality. We also show that the results presented in this paper are the extensions of some existing results.
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    Some Milne's rule type inequalities in quantum calculus
    (Univ Nis, Fac Sci Math, 2023) Sial, Ifra Bashir; Budak, Hüseyin; Ali, Muhammad Aamir
    The main goal of the current study is to establish some new Milne's rule type inequalities for single-time differentiable convex functions in the setting of quantum calculus. For this, we establish a quantum integral identity and then we prove some new inequalities of Milne's rule type for quantum differentiable convex functions. These inequalities are very important in Open-Newton's Cotes formulas because, with the help of these inequalities, we can find the bounds of Milne's rule for differentiable convex functions in classical or quantum calculus. The method adopted in this work to prove these inequalities are very easy and less conditional compared to some existing results. Finally, we give some mathematical examples to show the validity of newly established inequalities.