Jensen Type Inequality for L-Gap Convex Functions

The concept of l -gap convex functions is defined, which is more general than convex functions and allows some non-convex parts of the function. A Jensen type inequality is established and some examples are discussed. As an application and generalization, we prove that the majorization theorem also holds for l -gap convex functions. Then we use the conclusions from the above sections to establish a Hermite-Hadamard type inequality for l -gap convex functions.