Simpson, midpoint, and trapezoid-type inequalities for multiplicatively s-convex functions

Abstract

In this study, we establish new generalizations and results for Simpson, midpoint, and trapezoid-type integral inequalities within the framework of multiplicative calculus. We begin by proving a new identity for multiplicatively differentiable functions. Using this identity, we then obtain a new Simpson-type inequality for multiplicatively ss-convex functions. Additionally, we derive novel integral inequalities related to the right and left sides of the Hermite-Hadamard inequality for multiplicatively ss-convex functions. We also demonstrate that some of the results obtained here improve upon known results, while others are generalizations. Finally, we present some applications to special means.

Keywords

• multiplicative calculus
• multiplicatively s-convex function
• simpson inequality
• midpoint-type inequality
• trapezoid-type inequality
• 26d07
• 26d10
• 26d15
• 26a51