Integral inequalities of Hermite – Hadamard type for $((\alpha,m), \log)$-convex functions on co–ordinates

The convexity of functions is a basic concept in mathematics and it has been generalized in various directions. Establishing integral inequalities of Hermite – Hadamard type for various convex functions is one of main topics in the theory of convex functions and attracts a number of mathematicians for several centuries. Currently there have accumulated an amount of literature on integral inequalities of Hermite – Hadamard type for various convex functions. In the paper, the authors introduce a new concept "$((\alpha,m), \log)$–convex functions on the co–ordinates on the rectangle of the plane" and establish new integral inequalities of the Hermite – Hadamard type for $((\alpha,m),\log)$-convex functions on the co–ordinates on the rectangle of the plane.