Interval valued Jensen’s inequalities for h-convex functions on time scales

Abstract

In the paper, we study dynamic h-convexity for interval valued functions. Some generalizations of Jensen’s inequality in interval valued analysis for h-convex functions on time scales are proved in the paper. In seek of applications of generalized Jensen’s inequality, Hermite-Hadamard type inequalities for h-convex functions on time scales are established. Further discrete analogues of newly proved results are also presented in the paper. Some numerical examples are also provided to check the validity of the results.

Keywords:

• h-convexity
• Hermite Hadamard inequality
• interval valued functions
• Jensen’s inequality
• time scales

MSC 2010:

• 28A25
• 28A78
• 28B15
• 26D15
• 34N05

Disclosure statement

No potential conflict of interest was reported by the authors.