Hermite-Hadamard-Fejer and Jensen-Type Inequalities for $\eta $-Convex Functions in the Non-Newtonian Setting

Abstract

\kjmAbstract{ We study the relation between $\eta_\alpha$-convex functions and the classical notion of $\eta$-convexity. A characterization of $\eta_\alpha$-convex functions is established, and several inequalities that follow from this characterization are derived. Using non-Newtonian calculus with a generator $\alpha$, we obtain new Hermite–Hadamard–Fejér and Jensen-type inequalities for $\eta$-convex functions. Further results are proved for $\alpha$-differentiable $\eta_\alpha$-convex functions, showing that these inequalities extend and generalize many classical results from the literature. }

Keywords

• Non-Newtonian calculus
• $\alpha$-convexity
• $\eta_\alpha$-convexity
• Hermite-Hadamard-Fejér inequalities
• Jensen

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