New Simpson's type inequalities via \((\alpha_1, m_1)\) -\((\alpha_2, m_2)\)- preinvexity on the coordinates in both the first and second sense

Abstract

In this paper, we established a new integral identity for twice partially differentiable functions. As a consequence, we established some new Simpson's type integral inequalities for functions of two independent variables whose mixed partial derivative is bounded and \((\alpha_1, m_1)-(\alpha_2, m_2)\)-preinvex on the coordinates in both the first and second sense.