Weighted Energy Estimates for Convex Functions, Convex Vectors and Subsolution of Partial Differential Equation

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The role of convex sets, convex function and their generalizations get rapid development due to its enormous use in applied mathematics specially in non-linear programming, optimization theory and hedging strategies. Due to the advancement in applied mathematics there was necessity to extend the notion of convexity.

The definition of convexity have deep relations with the theory of inequalities because the definition of convex function is itself an inequality and many important inequalities follows from convexity.