New Hermite-Hadamard type inequalities for m and (a, m)-convex functions on the coordinates via generalized fractional integrals.

FRACTIONAL integrals; INTEGRAL inequalities; GENERALIZED integrals; CONVEX functions; ABSOLUTE value; INDEPENDENT variables

In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (a, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables. [ABSTRACT FROM AUTHOR]

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