Jensen-Type Inequalities for Divided Differences via Generalized Convex Functions

Key Points

• This research aims to extend Jensen's inequality through the lens of generalized convex functions and divided differences.
• Utilized (m + 4)-convex functions to derive estimates for Jensen's inequality.
• Extended results to (h, g; α−n)-convex functions.
• Examined properties of g-convex functions and (h, g)-convex functions.
• Derived new estimates for Jensen's inequality applicable to divided differences.
• Established connections between different types of convex functions and Jensen's inequality.
• Provided examples and discussions highlighting the applicability of h-convex functions.