New Convex Function Inequalities and Generalizations of Bernoulli s Inequality

Key Points

• The research aims to extend classical characterizations of convex functions through new inequalities.
• Developed a generalized equivalence result for convex functions.
• Utilized classical convexity tools and right-hand derivative analysis.
• Employed simpler proof techniques to avoid complex arguments.
• Introduced new functional inequalities of Bernoulli type.
• Demonstrated stronger results compared to previous characterizations.