In this manuscript, we give and study the concept of exponential type convex functions and some of their algebraic properties. We prove two Hermite-Hadamard (H-H) type integral inequalities for the newly introduced class of functions. We also obtain some refinements of the H-H inequality for functions whose first derivative in absolute value at certain power is exponential type convex.
In this work, by using an integral identity together with both the Hölder and the Power-mean integral inequalities we establish several new inequalities for n-times differentiable convex and concave mappings.
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