FIXED-POINT THEOREMS IN METRIC SPACES: APPLICATIONS TO NONLINEAR INTEGRAL EQUATIONS

This study explores their utility in solving nonlinear integral equations, a class of equations frequently encountered in mathematical modeling of physical, biological, and engineering systems.We provide a comprehensive review of key fixed-point theorems, including Banach's Contraction Principle, Schauder's Fixed-Point Theorem, and their generalizations.Emphasis is placed on the conditions under which these theorems can be applied to nonlinear integral equations.Examples demonstrate the practical implementation of these theorems to guarantee the existence and uniqueness of solutions.The results highlight the interplay between the structure of metric spaces, operator properties, and the formulation of integral equations, offering a robust framework for tackling nonlinear problems across diverse applications.