Beyond classical convexity: super-quadratic convex mappings and their inequality framework

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 73 - 30
• Main Authors: Javed, Muhammad Zakria, Arshad, Amina, Awan, Muhammad Uzair, Almalki, Yahya, Breaz, Daniel, Cotîrlă, Luminiţa-Ioana, Danciu, Alin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 13.06.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Control theory; Convexity; Hadamard’s inequality; Hermite; Inequality; Information theory; Jensen; Jensen’s inequality; Mathematics; Mathematics and Statistics; Mercer inequality; Operators (mathematics); Optimization; Super-quadratic mapping; Jensen; Jensen’s inequality; Hadamard’s inequality; 26A51; 26D20; 26D10; 26A33; Super-quadratic mapping; Fractional calculus; Hermite; Mercer inequality; 26D07; 26D15

This study investigates a new class of totally ordered interval-valued super-quadratic convex mappings that are based on the ordering relation c r and control mappings ħ . We also discuss a few captivating properties of this class, along with some special cases, to ensure its broadness and utility....