![]() Besides these, the existence and asymptotical stability are proven. As the last stage, the definitions of global attractivity and asymptotical stability for equations on Banach space B C ( R + ) are given while proving the existence of solutions and global attractivity. In addition, the proof of the existence of global attractors and asymptotic stabilities, having at least one solution which pertains to B C ( R + ) is looked into. Hence, the aim is to study nonlinear functional-integral equations in the Banach space B C ( R + ) using the measure of noncompactness. Subsequently, the definition of the measure pertaining to noncompactness on Banach space along with properties is presented. The existence results of the equations are generally obtained based on fundamental methods by which the fixed-point theorems are frequently applied. ![]() Besides, proving the existence and uniqueness of the solutions by the Banach theorem is carried out. Accordingly, this study provides the basic definitions and results regarding Banach spaces with the proof as well as applications. Nonlinear science serves to reveal the nonlinear descriptions of widely different systems, has had a fundamental impact on complex dynamics. Nonlinear functional-integral equations contain the unknown function nonlinearly, occurring extensively in theory developed to a certain extent toward different applied problems and solutions thereof.
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