The study of the existence of positive solutions of operator equations in ordered Banach spaces, in which algebra, geometry and analysis are combined, has received much attention in the past few decades, but still in the present time.It is related to the existence of positive solutions of operator equations that have been raised in application, such as buckling of mechanical structures, design of suspension bridges, steady-state temperature distribution, chemical reactions, interaction between predators and prey, and management of natural resources.This problem can be reduced to the existence...