In this paper, authors study the concept of (s, m)–exponential type convex functions and their algebraic properties. New generalizations of Hermite–Hadamard type inequality for the (s, m)–exponential type convex function ψ and for the products of two (s, m)–exponential type convex functions ψ and φ are proved. Some refinements of the (H–H) inequality for functions whose first derivative in absolute value at certain power are (s, m)–exponential type convex are obtain. Finally, many new bounds for special means and new error estimates for the trapezoidal and midpoint formula are provided as well.