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On new generalized fractional midpoint-type inequalities for co-ordinated convex and co-ordinated concave functions
(Univ Nis, 2023) Yildirim, Seda Kilinc; Kara, Hasan; Budak, Hüseyin; Yildirim, Hüseyin
In this paper, we firstly obtain a new generalized identity for twice partially differentiable functions Riemann-Liouville fractional integrals. Then, using this equality, we obtain some midpoint-type inequalities for co-ordinated convex and co-ordinated concave functions. We also show that our result generalizes the give several inequalities obtained in earlier works.
On new generalized inequalities with some parameters for coordinated convex functions via generalized fractional integrals
(Wiley, 2021) Budak, Hüseyin; Yildirim, Seda Kilinc; Kara, Hasan; Yildirim, Hüseyin
In this work, firstly, we obtain a new identity with some parameters for generalized fractional integrals. Then by utilizing this obtained equality, we establish some new parameterized inequalities for coordinated convex functions via generalized fractional integrals. In addition, in a separate section, we show that the results given in the main section reduce to several trapezoid, midpoint, and Simpson type inequalities for various values of parameters.