Generalization of the Wolstenholme cyclic inequality and its application

This paper deals with the generalization and sharp versions of the Wolstenholme cyclic inequality and their applications. The inequalities of this paper improve and unify corresponding known results. Several interesting inequalities including the celebrated Ozeki inequality are obtained. Extensions of the Wolstenholme inequality for a complex polygon and the Wolstenholme inequality for a convex quadrilateral are derived. As example of applications, the well-known Erdös–Mordell inequality is improved in this paper. In addition, several extensions, unifications and refinements of Gueron–Shafrir’s inequalities and Mitrinović–Pecaric’s inequality are established.