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Some New Hermite-Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral
Miguel Vivas-Cortez1, Muhammad Aamir Ali2, Hüseyin Budak3
1Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, University of Buenos Aires, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador.
Abstract:
In this investigation, for convex functions, some new (p,q)-Hermite-Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)π2 integral are offered. It is also shown that the newly proved results for p=1 and q→1- can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.
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