Hyers‐Ulam‐Rassias stability of nonlinear integral equations through the Bielecki metric

Abstract

We analyse different kinds of stabilities for classes of nonlinear integral equations of Fredholm and Volterra type. Sufficient conditions are obtained in order to guarantee Hyers‐Ulam‐Rassias, σ‐semi‐Hyers‐Ulam and Hyers‐Ulam stabilities for those integral equations. Finite and infinite intervals are considered as integration domains. Those sufficient conditions are obtained based on the use of fixed point arguments within the framework of the Bielecki metric and its generalizations. The results are illustrated by concrete examples.

On the Generalized Hyers–Ulam Stability of a Functional Equation and Its Consequences

“…In recent years, the Hyers-Ulam stability of several objects (for instance functional equations and inequalities, isometries, differential, difference, integral and integro-differential equations, flows, groups, vector measures, and C*algebras) has been studied by many researchers (for more information on this notion as well as its applications we refer the reader to papers [1][2][3]5,8,9,[12][13][14]16,[18][19][20][24][25][26]30] and books [7,23]).…”

Hyers-Ulam stability of a certain Fredholm integral equation

“…by fixed point Theorem. Recently, only few authors are investigating the Hyers-Ulam stability of the various integral equations (see [3,6,7,11,12,26,27]). Motivated by the above ideas, our foremost aim is to study the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of the certain Fredholm Integral equations of second kind…”

Stability of Nonlocal Stochastic Volterra Equations

“…The study of Volterra differential and integral equations with classical initial conditions have been of interest due to their several applications in various fields of science such as semiconductors, population dynamics, heat conduction, fluid flow, etc., see [1,2,7,[9][10][11][12][13][14][15][16][17][18][19][20]23]. Differential equations with nonlocal and functional conditions have become an active area of research.…”

“…Some properties of the solutions to differential equations of Volterra type were studied by [2,8,9,11,12,14,16,17,23]. [7,8,[10][11][12] analised some types of stability (Ulam, Hyers-Ulam, and Hyers-Ulam-Rassias) for nonlinear integro-differential Volterra equations and Volterra integral equations by using fixed-point arguments and the Bielecki metric techniques. [14] extended the work of [8] to a class of nonlinear stochastic integral equation of Volterra type.…”