Hermite-Hadamard-type inequalities for generalized trigonometrically and hyperbolic ρ-convex functions in two dimension

In this article, we establish Hermite-Hadamard-type inequalities for the two classes of functions X-+/-lambda (Omega) = {f is an element of C-2(Omega) : Delta f +/- lambda f >= 0}, where lambda > 0 and Omega is an open subset of R-2. We also obtain a characterization of the set X-lambda (Omega). Notice that in the one-dimensional case, if Omega = I (an open interval of R) and lambda = rho(2), rho > 0, then X-lambda (Omega) reduces to the class of functions f is an element of C-2 (I) such that f is trigonometrically rho-convex (resp. hyperbolic rho-convex) on I.