Malaysian Journal of Mathematical Sciences, March 2025, Vol. 19, No. 1
A Fractional Version of Corrected Dual-Simpson's Type Inequality via $s-$convex Function with Applications
Munir, A., Qayyum, A., Budak, H., Qaisar, S., Ali, U., and Supadi, S. S.
Corresponding Email: [email protected]
Received date: 15 March 2024
Accepted date: 13 August 2024
Abstract:
Convexity plays a crucial role in mathematical analysis, offering profound insights into the behavior of functions and geometric shapes. Fractional integral operators generalize the classical concept of integration to non-integer orders. In this paper, we establish a new identity by using the Caputo--Fabrizio fractional integral operator. Then by using this new identity, we obtain the corrected dual Simpson's type inequalities for $s-$convex functions. By employing the well-known integral inequalities such as the Hölder's inequality and power-mean inequality, we obtain new error estimates. Furthermore, we discuss the applications to some special means and quadrature formula.
Keywords: corrected dual-Simpson's type inequality; $s-$convex function; fractional integrals; Hölder's inequality; power-mean inequality
