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In this paper we prove some Hermite-Hadamard, Fejer and Sherman type inequlities for generalizations of superquadratic functions and convex functions. These results, under a monotonicity condition, lead to refinements of the Hermite-Hadamard, Fejer and Sherman inequalities of non-negative convex functions. Also, the obtained inequalities are discussed about and compared with some recent generalizations of weighted Hermite-Hadamard inequalities. Mathematics subject classification (2010): 26D15, 94A17.

Hermite-Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions