Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality

Abstract

In the paper, we consider functional set-valued integral equations whose representation contains set-valued integrals occurring symmetrically on both sides of the equation. On the coefficients of the equation, we impose certain conditions, more general than the standard Lipschitz condition, which allow the application of the Bihari–LaSalle inequality in the proofs of the obtained theorems. In this way, we obtain a result about the existence and uniqueness of the solution of the equation under consideration and the insensitivity of the solution in the case of minor changes in the parameters of the equation.

Keywords

• set-valued integral equations
• existence and uniqueness of solution
• Bihari–LaSalle inequality