Jensen Type Inequality for L-Gap Convex Functions

Key Points

• The aim is to define l-gap convex functions and establish a Jensen type inequality for them.
• Defined l-gap convex functions as a generalization of convex functions.
• Established a Jensen type inequality for l-gap convex functions.
• Proved that the majorization theorem applies to l-gap convex functions.
• Developed a Hermite-Hadamard type inequality for l-gap convex functions.
• Established a new Jensen type inequality specific to l-gap convex functions.
• Confirmed that the majorization theorem is valid for the new function class.
• Derived a Hermite-Hadamard inequality that extends to l-gap convex functions.