On Uniformly δ-Geometric Convex Functions

Key Points

• The aim is to develop new inequalities and bounds related to uniformly δ-geometric convex functions.
• Introduced new Jensen, Jensen–Mercer, and Hermite–Hadamard inequalities for uniformly δ-geometric convex functions.
• Established limit bounds for Caputo–Fabrizio fractional integral operators in this context.
• Provided examples and graphical representations to illustrate the results.
• Demonstrated new inequalities that expand the existing understanding of uniformly δ-geometric convex functions.
• Established limit bounds for fractional integrals that apply specifically to these functions.
• Illustrated validity through examples, reinforcing the theoretical contributions.