Unified discrete and integral Giaccardi inequalities under the isotonic linear functionals and their applications in different time scales

Abstract

Abstract This article introduces the Giaccardi inequality using isotonic linear functionals and h-convexity. This work includes both discrete and integral variants of this inequality. The important Petrović inequality is deduced as a special case. For some applications, the established inequalities are extended to time scales.

Keywords

• Giaccardi inequality
• Time scale
• Petrović inequality
• h-convex function
• Isotonic functional