On the Ulam stabilities of nonlinear integral equations and integro‐differential equations
Osman Tunç, Cemil Tunç, Gabriela Petruşel, Jen‐Chih Yao
Abstract
In this research, two systems of nonlinear Volterra integral equation and Volterra integro‐differential equation were considered. New results in sense of Ulam stabilities in relation to these two systems were proved on a finite interval. The proof of the results on the Ulam stabilities of that classes of the equations are based on the nonlinear alternative related to Banach's contraction principle. The outcomes of this research give new contribution to the theory of Ulam stabilities.
Topics & Concepts
MathematicsContraction principleNonlinear systemIntegro-differential equationIntegral equationVolterra integral equationDifferential equationMathematical analysisContraction (grammar)Banach spaceApplied mathematicsFixed-point theoremFirst-order partial differential equationInternal medicinePhysicsQuantum mechanicsMedicineFunctional Equations Stability ResultsNumerical methods for differential equationsMathematical and Theoretical Analysis