Existence and uniqueness of a positive solutions for the product of operators

Abstract

In this paper, we prove the existence of a positive solution for some equations involving multiplication of concave (possibly nonlinear) operators. Also, we provide a successively sequence to approximate the solution for such equations. This kind of the solution is necessary for quadratic differential and integral equations.

Keywords

• fixed point
• product of operator
• quadratic integral equation
• positive solution
• concave operator