REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.112, no.4, pp.969-992, 2018 (SCI-Expanded)
In this paper, we prove the correct (p, q)-Hermite-Hadamard inequality, some new (p, q)-Hermite-Hadamard inequalities, and generalized (p, q)-Hermite-Hadamard inequality. By using the left hand part of the correct (p, q)-Hermite-Hadamard inequality, we have a new equality. Finally using the new equality, we give some (p, q)-midpoint type integral inequalities through (p, q)-differentiable convex and (p, q)-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works.