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Fractional Ostrowski type inequalities for differentiable harmonically convex functions
(Amer Inst Mathematical Sciences-Aims, 2022) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Budak, Hüseyin; Ntouyas, Sotiris K.; Promsakon, Chanon
In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.
On generalizations of quantum Simpson's and quantum Newton's inequalities with some parameters
(Amer Inst Mathematical Sciences-Aims, 2021) Promsakon, Chanon; Ali, Muhammad Aamir; Budak, Huseyin; Abbas, Mujahid; Muhammad, Faheem; Sitthiwirattham, Thanin
In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new Simpson's and Newton's type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old Simpson's type inequalities, Newton's type inequalities, midpoint type inequalities, and trapezoidal type inequalities.