Convexity, Its Variations, and Related Integral Inequalities

Abstract

This study explores the concept of convexity, its various generalized forms, and their relationships with integral inequalities in mathematical analysis. The research focuses on investigating different classes of convex functions and extending classical convexity concepts through advanced analytical approaches. Several integral inequalities associated with these variations are derived and analyzed under different conditions. The obtained results contribute to the theoretical development of convex analysis and provide broader applications in optimization theory, numerical analysis, economics, and applied mathematics. The study highlights the importance of generalized convexity in establishing new mathematical inequalities and solving complex analytical problems.