协同(r,(h,m))-凸函数的Hermite-Hadamard型积分不等式

Hermite-Hadamard Type Integral Inequality for Coordinated (r,(h,m))-Convex Function

摘要: Hermite-Hadamard不等式是凸函数中重要不等式之一，其积分误差估计在优化问题、计算问题等中有着很重要的应用，多元函数的协同凸性的概念引进以来，使得凸性理论进一步发展，本文将定义一个新的二元函数，且其一个分量满足r-凸性，另一个分量为广义(h,m)-凸性的协同(r,(h,m))-凸函数，并研究其Hermite-Hadamard型积分不等式。

Abstract: Hermite-Hadamard inequality is one of the most important inequalities in convex functions. Its integral error estimates have important applications in optimization and computation. Since the concept of co-convexity of multivariate functions was introduced, the convexity theory has been further developed. In this paper, a new binary function is defined, coordinated (r,(h,m))-convex functions of bivariate functions, one of whose components is r-convex and the other is extended (h,m)-convex; Hermite-Hadamard type integral inequalities are studied.