The weighted discrete dynamic inequalities for 4-convex functions, and its generalization on time scales with constant graininess function

Abstract

Abstract Motivated by Pečarić et al. in (J. Math. Inequal. 11(2):543–5502017), we established here weighted discrete dynamic inequalities for the difference of second divided difference of 4-convex functions. Further we extend and unify the two inequalities, by establishing the theory of n-convexity on time scales having constant graininess function.

Keywords

• The weighted delta-integral estimates
• 4-convex function
• Time scales