<p>Integral inequalities involving exponential convexity are significant in both theoretical and applied mathematics. In this paper, we establish a new Hermite-Hadamard type inequality for the class of exponentially convex functions by using the concept of $ (\alpha-s) $ exponentially convex function. Additionally, using the well-known Hermite-Hadamard and Ostrowski inequalities, we establish several new integral inequalities. These newly obtained results contain several well-known results as special cases. Finally, new estimations for the trapezoidal formula have been provided, illustrating the practical applications of the research.</p>