Hermite-Hadamard and Ostrowski type inequalities via $\alpha$-exponential type convex functions with applications

This paper introduced and investigated a new form of convex mapping known as $\alpha$-exponential type convexity. We presented several algebraic properties associated with this newly introduced convexity. Additionally, we established novel adaptations of well-known inequalities, including the Hermite-Hadamard and Ostrowski-type inequalities, specifically for this convex function. We also derived special cases of these newly established results. Furthermore, we provided new estimations for the trapezoidal formula, demonstrating practical applications of this research.