On Stability Analysis of Solutions for a Class of Nonlinear Integral Equations in Banach Algebra

In this study, the existence of a solution of a class of operator equations given as the product of two operators in Banach algebra \(BC\left ( \mathbb {R} _{+}\right ) \) is examined. For this purpose, fixed-point theory is used as the main tool. In addition, via measure noncompactness (MNC) that is used associated with the fixed-point theorem, some results are given about how the solutions will behave if the independent variable increases unlimitedly. Finally, some examples of equations are presented to show the applicability of the obtained results.